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C23×#1878 #15669497

order2944
nilpotency class3
automorphism?
homologyAbelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C24

Aliases

direct productC23×#1878

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

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 2944

A minimal faithful permutation representation — 3 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,27)(28,29)(30,31)(32,33,36,38,37,41,35,40)(34,42,44,39,45,46,43,47);(24,25,26,27)(33,38)(35,36)(39,42)(40,41)(43,44)(46,47);(29,31)(32,34,37,45)(33,39,41,47)(35,44,36,43)(38,42,40,46)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C23×#1878, C23×#20924, C23×#20926, …
maximal normal subgroup ofC2×C23×#1878, C23×#20924, C23×#20926, …
maximal quotient ofC23×#8946, C23×#8950, C23×#8974, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 610);