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<Chapter Label="chap:constructions">
<Heading>Functions for Character Table Constructions</Heading>
<#Include Label="construc:intro">
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<Section Label="sec:construc:MGA">
<Heading>Character Tables of Groups of Structure <M>M.G.A</M></Heading>
For the functions in this section,
let <M>H</M> be a group with normal subgroups <M>N</M> and <M>M</M>
such that <M>H/N</M> is cyclic, <M>M \leq N</M> holds,
and such that each irreducible character of <M>N</M>
that does not contain <M>M</M> in its kernel
induces irreducibly to <M>H</M>.
(This is satisfied for example if <M>N</M> has prime index in <M>H</M>
and <M>M</M> is a group of prime order that is central in <M>N</M>
but not in <M>H</M>.)
Let <M>G = N/M</M> and <M>A = H/N</M>,
so <M>H</M> has the structure <M>M.G.A</M>.
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<Section Label="sec:construc:GS3">
<Heading>Character Tables of Groups of Structure <M>G.S_3</M></Heading>
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<Section Label="sec:construc:GV4">
<Heading>Character Tables of Groups of Structure <M>G.2^2</M></Heading>
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<Section Label="sec:construc:V4G">
<Heading>Character Tables of Groups of Structure <M>2^2.G</M></Heading>
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<Section Label="sec:construc:subdirindex2">
<Heading>Character Tables of Subdirect Products of Index Two</Heading>
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<Section Label="sec:construc:functions">
<Heading>Construction Functions used in the Character Table Library</Heading>
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