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C2×C23×#498 #15670776

order2944
nilpotency class3
isoclinismisoclinic class of #465
automorphism?
homologyAbelianization (H1) = C24×C23 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×C23×#498

Subgroups

subgroupG/H
center, socle, prime radicalC23×C23C2×D4
commutator, Frattini, cosocleC2×C4C24×C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G

424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 2944

A minimal faithful permutation representation — 4 generators on 41 points:

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

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#9059, C23×#9729, C23×#9741, …
maximal normal subgroup ofC23×#9059, C23×#9729, C23×#9741, …
maximal quotient ofC2×C23×#1844, C2×C23×#1941, C2×C23×#1990, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1889);