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C23×#2973 #15670592

order2944
nilpotency class2
automorphism?
homologyAbelianization (H1) = C23×C4×C23 · Schur multiplier (H2) = C24

Aliases

direct productC23×#2973

Subgroups

subgroupG/H
centerC2×C4×C23C24
commutatorC22C23×C4×C23
Frattini, cosocleC2×C4C24×C23
socleC22×C23C23×C4
prime radicalC22×D4×C23C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C23 ◁ G

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 736

A minimal faithful permutation representation — 4 generators on 39 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)(26,30)(27,29)(28,31)(32,33,34,37,35,36,38,39);(24,26)(25,28)(27,31)(29,30);(26,31)(28,30)(33,36)(37,39);(25,29)(28,30)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#8852, C23×#8859, C23×#8864, …
maximal normal subgroup ofC23×#8852, C23×#8859, C23×#8864, …
maximal quotient ofC23×#20524, C23×#20526, C23×#20534, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1705);