Finite Group Databasebeta

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C23×#2713 #15670332

order2944
nilpotency class2
isoclinismisoclinic class of #2668
automorphism?
homologyAbelianization (H1) = C24×C23 · Schur multiplier (H2) = C24

Aliases

direct productC23×#2713

Subgroups

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

432 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)(29,32)(30,34)(36,37,40,42)(38,39,43,41);(25,27)(29,32)(33,35)(36,38,40,43)(37,41,42,39);(24,25)(26,27)(28,29,31,32)(30,33,34,35);(28,30)(29,33)(31,34)(32,35)(36,39,40,41)(37,38,42,43)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#36742, C23×#36743, C23×#36751, …
maximal normal subgroup ofC23×#36742, C23×#36743, C23×#36751, …
maximal quotient ofC23×#14378, C23×#14404, C23×#14406, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1445);