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C23×#2331 #15669950

order2944
nilpotency class2
automorphism?
homologyAbelianization (H1) = C23×C4×C23 · Schur multiplier (H2) = C23×C4

Aliases

direct productC23×#2331

Subgroups

subgroupG/H
center, socle, prime radicalC23×C23C24
commutatorC22C23×C4×C23
Frattini, cosocleC23C24×C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C23 ◁ G

460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 2944

A minimal faithful permutation representation — 4 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,27,26)(28,29,31,32)(30,34,35,33)(38,42)(40,43);(24,26,27,25)(29,32)(33,34)(36,37,39,41)(38,40,42,43);(28,29)(30,33)(31,32)(34,35)(36,38,39,42)(37,40,41,43);(28,30,31,35)(29,33,32,34)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#9297, C23×#9298, C23×#9301, …
maximal normal subgroup ofC23×#9297, C23×#9298, C23×#9301, …
maximal quotient ofC23×#13779, C23×#13783, C23×#13792, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1063);