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C23×#2320 #15669939

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

Aliases

direct productC23×#2320

Subgroups

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

444 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)(24,25,26,27)(29,32)(33,35)(37,39)(38,42);(36,37,40,39)(38,43,42,41);(28,29)(30,33)(31,32)(34,35)(36,38,40,42)(37,41,39,43);(28,30,31,34)(29,33,32,35)(36,39,40,37)(38,43,42,41)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#9328, C23×#9330, C23×#17601, …
maximal normal subgroup ofC23×#9328, C23×#9330, C23×#17601, …
maximal quotient ofC23×#13781, C23×#13783, C23×#13786, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1052);