#
# Calculating a nilpotent quotient
# Nilpotency class: 20
# Size of exponents: 8 bytes
#
# Calculating the abelian quotient ...
# The abelian quotient has 3 generators
# with the following exponents: 0 0 0
#
# Calculating the class 2 quotient ...
## Sizes: 3 6
# Maximal entry: 0
# Layer 2 of the lower central series has 2 generators
# with the following exponents: 0 0
#
# Calculating the class 3 quotient ...
## Sizes: 3 5 12
# Maximal entry: 0
# Layer 3 of the lower central series has 1 generators
# with the following exponents: 0
#
# Calculating the class 4 quotient ...
## Sizes: 3 5 6 15
# Maximal entry: 0
# Layer 4 of the lower central series has 1 generators
# with the following exponents: 2
#
# Calculating the class 5 quotient ...
## Sizes: 3 5 6 7 19
# Maximal entry: 1
# Layer 5 of the lower central series has 2 generators
# with the following exponents: 2 2
#
# Calculating the class 6 quotient ...
## Sizes: 3 5 6 7 9 27
# Maximal entry: 4
# Layer 6 of the lower central series has 1 generators
# with the following exponents: 2
#
# Calculating the class 7 quotient ...
## Sizes: 3 5 6 7 9 10 31
# Maximal entry: 4
# Layer 7 of the lower central series has 1 generators
# with the following exponents: 2
#
# Calculating the class 8 quotient ...
## Sizes: 3 5 6 7 9 10 11 35
# Maximal entry: 5
# Layer 8 of the lower central series has 1 generators
# with the following exponents: 2
#
# Calculating the class 9 quotient ...
## Sizes: 3 5 6 7 9 10 11 12 39
# Maximal entry: 4
# Layer 9 of the lower central series has 1 generators
# with the following exponents: 2
#
# Calculating the class 10 quotient ...
## Sizes: 3 5 6 7 9 10 11 12 13 43
# Maximal entry: 18
# Layer 10 of the lower central series has 1 generators
# with the following exponents: 2
#
# Calculating the class 11 quotient ...
## Sizes: 3 5 6 7 9 10 11 12 13 14 47
# Maximal entry: 11
# Layer 11 of the lower central series has 1 generators
# with the following exponents: 2
#
# Calculating the class 12 quotient ...
## Sizes: 3 5 6 7 9 10 11 12 13 14 15 51
# Maximal entry: 12
# Layer 12 of the lower central series has 1 generators
# with the following exponents: 2
#
# Calculating the class 13 quotient ...
## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 55
# Maximal entry: 15
# Layer 13 of the lower central series has 1 generators
# with the following exponents: 2
#
# Calculating the class 14 quotient ...
## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 17 59
# Maximal entry: 20
# Layer 14 of the lower central series has 1 generators
# with the following exponents: 2
#
# Calculating the class 15 quotient ...
## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 17 18 63
# Maximal entry: 30
# Layer 15 of the lower central series has 1 generators
# with the following exponents: 2
#
# Calculating the class 16 quotient ...
## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 17 18 19 67
# Maximal entry: 44
# Layer 16 of the lower central series has 1 generators
# with the following exponents: 2
#
# Calculating the class 17 quotient ...
## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 71
# Maximal entry: 52
# Layer 17 of the lower central series has 1 generators
# with the following exponents: 2
#
# Calculating the class 18 quotient ...
## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 21 75
# Maximal entry: 175
# Layer 18 of the lower central series has 1 generators
# with the following exponents: 2
#
# Calculating the class 19 quotient ...
## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 21 22 79
# Maximal entry: 175
# Layer 19 of the lower central series has 1 generators
# with the following exponents: 2
#
# Calculating the class 20 quotient ...
## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 83
# Maximal entry: 434
# Layer 20 of the lower central series has 1 generators
# with the following exponents: 2
#
# The epimorphism :
# e1 |---> A
# e2 |---> B
# e3 |---> C
# The nilpotent quotient :
<A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X
|
G^2 = H*I*L,
H^2 = K*L*M*N*O*P*Q*R*S*T*U*V*W*X,
I^2 = K,
J^2 = L,
K^2 = M,
L^2 = N,
M^2 = O,
N^2 = P,
O^2 = Q,
P^2 = R,
Q^2 = S,
R^2 = T,
S^2 = U,
T^2 = V,
U^2 = W,
V^2 = X,
W^2,
X^2,
B^A =: B*D,
B^(A^-1) = B*D^-1,
C^A = C,
C^(A^-1) = C,
C^B =: C*E,
C^(B^-1) = C*E^-1,
D^A = D,
D^(A^-1) = D,
D^B = D,
D^(B^-1) = D,
D^C = D*F^-1*G*J*L*N*P*R*T*V*X,
D^(C^-1) = D*F*G*H*J*K,
E^A =: E*F,
E^(A^-1) = E*F^-1*H,
E^B = E,
E^(B^-1) = E,
E^C = E,
E^(C^-1) = E,
E^D = E*G*I*J*K*L*M*N*O*P*Q*R*S*T*U*V*W*X,
E^(D^-1) = E*G*H,
F^A = F*H*K*L,
F^(A^-1) = F*H*K*L,
F^B =: F*G,
F^(B^-1) = F*G*H*I*J,
F^C = F,
F^(C^-1) = F,
F^D = F*H*K*L,
F^(D^-1) = F*H*K*L,
F^E = F*I*J,
F^(E^-1) = F*I*J,
G^A =: G*H,
G^(A^-1) = G*H,
G^B = G*J*L*N*P*R*T*V*X,
G^(B^-1) = G*J*L*N*P*R*T*V*X,
G^C =: G*I,
G^(C^-1) = G*I,
G^D = G*J*L*N*P*R*T*V*X,
G^(D^-1) = G*J*L*N*P*R*T*V*X,
G^E = G*J*L*N*P*R*T*V*X,
G^(E^-1) = G*J*L*N*P*R*T*V*X,
G^F = G,
G^(F^-1) = G,
H^A = H*K*L,
H^(A^-1) = H*K*L,
H^B = H*J,
H^(B^-1) = H*J,
H^C = H,
H^(C^-1) = H,
H^D = H*K*L,
H^(D^-1) = H*K*L,
H^E = H*K*L,
H^(E^-1) = H*K*L,
H^F = H,
H^(F^-1) = H,
H^G = H,
I^A = I,
I^(A^-1) = I,
I^B =: I*J,
I^(B^-1) = I*J,
I^C = I*K*M*O*Q*S*U*W,
I^(C^-1) = I*K*M*O*Q*S*U*W,
I^D = I*K*M*O*Q*S*U*W,
I^(D^-1) = I*K*M*O*Q*S*U*W,
I^E = I*K*M*O*Q*S*U*W,
I^(E^-1) = I*K*M*O*Q*S*U*W,
I^F = I,
I^(F^-1) = I,
I^G = I,
I^H = I,
J^A = J*K*L*M*N*O*P*Q*R*S*T*U*V*W*X,
J^(A^-1) = J*K*L*M*N*O*P*Q*R*S*T*U*V*W*X,
J^B = J*L*N*P*R*T*V*X,
J^(B^-1) = J*L*N*P*R*T*V*X,
J^C =: J*K,
J^(C^-1) = J*K,
J^D = J*L*N*P*R*T*V*X,
J^(D^-1) = J*L*N*P*R*T*V*X,
J^E = J*L*N*P*R*T*V*X,
J^(E^-1) = J*L*N*P*R*T*V*X,
J^F = J,
J^(F^-1) = J,
J^G = J,
J^H = J,
J^I = J,
K^A = K,
K^(A^-1) = K,
K^B =: K*L,
K^(B^-1) = K*L,
K^C = K*M*O*Q*S*U*W,
K^(C^-1) = K*M*O*Q*S*U*W,
K^D = K*M*O*Q*S*U*W,
K^(D^-1) = K*M*O*Q*S*U*W,
K^E = K*M*O*Q*S*U*W,
K^(E^-1) = K*M*O*Q*S*U*W,
K^F = K,
K^(F^-1) = K,
K^G = K,
K^H = K,
K^I = K,
K^J = K,
L^A = L*M*N*O*P*Q*R*S*T*U*V*W*X,
L^(A^-1) = L*M*N*O*P*Q*R*S*T*U*V*W*X,
L^B = L*N*P*R*T*V*X,
L^(B^-1) = L*N*P*R*T*V*X,
L^C =: L*M,
L^(C^-1) = L*M,
L^D = L*N*P*R*T*V*X,
L^(D^-1) = L*N*P*R*T*V*X,
L^E = L*N*P*R*T*V*X,
L^(E^-1) = L*N*P*R*T*V*X,
L^F = L,
L^(F^-1) = L,
L^G = L,
L^H = L,
L^I = L,
L^J = L,
L^K = L,
M^A = M,
M^(A^-1) = M,
M^B =: M*N,
M^(B^-1) = M*N,
M^C = M*O*Q*S*U*W,
M^(C^-1) = M*O*Q*S*U*W,
M^D = M*O*Q*S*U*W,
M^(D^-1) = M*O*Q*S*U*W,
M^E = M*O*Q*S*U*W,
M^(E^-1) = M*O*Q*S*U*W,
M^F = M,
M^(F^-1) = M,
M^G = M,
M^H = M,
M^I = M,
M^J = M,
M^K = M,
M^L = M,
N^A = N*O*P*Q*R*S*T*U*V*W*X,
N^(A^-1) = N*O*P*Q*R*S*T*U*V*W*X,
N^B = N*P*R*T*V*X,
N^(B^-1) = N*P*R*T*V*X,
N^C =: N*O,
N^(C^-1) = N*O,
N^D = N*P*R*T*V*X,
N^(D^-1) = N*P*R*T*V*X,
N^E = N*P*R*T*V*X,
N^(E^-1) = N*P*R*T*V*X,
N^F = N,
N^(F^-1) = N,
N^G = N,
N^H = N,
N^I = N,
N^J = N,
N^K = N,
N^L = N,
N^M = N,
O^A = O,
O^(A^-1) = O,
O^B =: O*P,
O^(B^-1) = O*P,
O^C = O*Q*S*U*W,
O^(C^-1) = O*Q*S*U*W,
O^D = O*Q*S*U*W,
O^(D^-1) = O*Q*S*U*W,
O^E = O*Q*S*U*W,
O^(E^-1) = O*Q*S*U*W,
O^F = O,
O^(F^-1) = O,
O^G = O,
O^H = O,
O^I = O,
O^J = O,
O^K = O,
O^L = O,
O^M = O,
P^A = P*Q*R*S*T*U*V*W*X,
P^(A^-1) = P*Q*R*S*T*U*V*W*X,
P^B = P*R*T*V*X,
P^(B^-1) = P*R*T*V*X,
P^C =: P*Q,
P^(C^-1) = P*Q,
P^D = P*R*T*V*X,
P^(D^-1) = P*R*T*V*X,
P^E = P*R*T*V*X,
P^(E^-1) = P*R*T*V*X,
P^F = P,
P^(F^-1) = P,
P^G = P,
P^H = P,
P^I = P,
P^J = P,
P^K = P,
P^L = P,
Q^A = Q,
Q^(A^-1) = Q,
Q^B =: Q*R,
Q^(B^-1) = Q*R,
Q^C = Q*S*U*W,
Q^(C^-1) = Q*S*U*W,
Q^D = Q*S*U*W,
Q^(D^-1) = Q*S*U*W,
Q^E = Q*S*U*W,
Q^(E^-1) = Q*S*U*W,
Q^F = Q,
Q^(F^-1) = Q,
Q^G = Q,
Q^H = Q,
Q^I = Q,
Q^J = Q,
Q^K = Q,
R^A = R*S*T*U*V*W*X,
R^(A^-1) = R*S*T*U*V*W*X,
R^B = R*T*V*X,
R^(B^-1) = R*T*V*X,
R^C =: R*S,
R^(C^-1) = R*S,
R^D = R*T*V*X,
R^(D^-1) = R*T*V*X,
R^E = R*T*V*X,
R^(E^-1) = R*T*V*X,
R^F = R,
R^(F^-1) = R,
R^G = R,
R^H = R,
R^I = R,
R^J = R,
S^A = S,
S^(A^-1) = S,
S^B =: S*T,
S^(B^-1) = S*T,
S^C = S*U*W,
S^(C^-1) = S*U*W,
S^D = S*U*W,
S^(D^-1) = S*U*W,
S^E = S*U*W,
S^(E^-1) = S*U*W,
S^F = S,
S^(F^-1) = S,
S^G = S,
S^H = S,
S^I = S,
T^A = T*U*V*W*X,
T^(A^-1) = T*U*V*W*X,
T^B = T*V*X,
T^(B^-1) = T*V*X,
T^C =: T*U,
T^(C^-1) = T*U,
T^D = T*V*X,
T^(D^-1) = T*V*X,
T^E = T*V*X,
T^(E^-1) = T*V*X,
T^F = T,
T^(F^-1) = T,
T^G = T,
U^A = U,
U^(A^-1) = U,
U^B =: U*V,
U^(B^-1) = U*V,
U^C = U*W,
U^(C^-1) = U*W,
U^D = U*W,
U^(D^-1) = U*W,
U^E = U*W,
U^(E^-1) = U*W,
U^F = U,
U^(F^-1) = U,
V^A = V*W*X,
V^(A^-1) = V*W*X,
V^B = V*X,
V^(B^-1) = V*X,
V^C =: V*W,
V^(C^-1) = V*W,
V^D = V*X,
V^(D^-1) = V*X,
V^E = V*X,
V^(E^-1) = V*X,
W^A = W,
W^(A^-1) = W,
W^B =: W*X,
W^(B^-1) = W*X,
W^C = W,
W^(C^-1) = W >
# Class : 20
# Nr of generators of each class : 3 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
# The definitions:
# D := [ B, A ]
# E := [ C, B ]
# F := [ C, B, A ]
# G := [ C, B, A, B ]
# H := [ C, B, A, B, A ]
# I := [ C, B, A, B, C ]
# J := [ C, B, A, B, C, B ]
# K := [ C, B, A, B, C, B, C ]
# L := [ C, B, A, B, C, B, C, B ]
# M := [ C, B, A, B, C, B, C, B, C ]
# N := [ C, B, A, B, C, B, C, B, C, B ]
# O := [ C, B, A, B, C, B, C, B, C, B, C ]
# P := [ C, B, A, B, C, B, C, B, C, B, C, B ]
# Q := [ C, B, A, B, C, B, C, B, C, B, C, B, C ]
# R := [ C, B, A, B, C, B, C, B, C, B, C, B, C, B ]
# S := [ C, B, A, B, C, B, C, B, C, B, C, B, C, B, C ]
# T := [ C, B, A, B, C, B, C, B, C, B, C, B, C, B, C, B ]
# U := [ C, B, A, B, C, B, C, B, C, B, C, B, C, B, C, B, C ]
# V := [ C, B, A, B, C, B, C, B, C, B, C, B, C, B, C, B, C, B ]
# W := [ C, B, A, B, C, B, C, B, C, B, C, B, C, B, C, B, C, B, C ]
# X := [ C, B, A, B, C, B, C, B, C, B, C, B, C, B, C, B, C, B, C, B ]
