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C23×#1921 #15669540

order2944
nilpotency class3
automorphism?
homologyAbelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C2×C4

Aliases

direct productC23×#1921

Subgroups

subgroupG/H
center, socle, prime radicalC23×C23C2×D4
commutatorC2×C4C22×C4×C23
Frattini, cosocleC22×C4C23×C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G

230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(30,33)(31,32)(34,35)(36,37,38,40)(39,41,43,42);(24,26,27,25)(29,32)(33,35)(37,40)(41,42);(28,30,31,34)(29,33,32,35)(37,41)(39,43)(40,42)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C23×#1921, C23×#21032, C23×#21033, …
maximal normal subgroup ofC2×C23×#1921, C23×#21032, C23×#21033, …
maximal quotient ofC23×#9536, C23×#9540, C23×#10807, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 653);