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C23×#2714 #15670333

order2944
nilpotency class2
isoclinismisoclinic class of #2668
automorphism?
homologyAbelianization (H1) = C24×C23 · Schur multiplier (H2) = C23×C4

Aliases

direct productC23×#2714

Subgroups

subgroupG/H
center, socleC23×C23C24
commutator, Frattini, cosocleC23C24×C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C23 ◁ G

598 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 1472

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

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#36741, C23×#36744, C23×#36758, …
maximal normal subgroup ofC23×#36741, C23×#36744, C23×#36758, …
maximal quotient ofC23×#14379, C23×#14396, C23×#14398, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1446);