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C23×#3251 #15670870

order2944
nilpotency class3
isoclinismisoclinic class of #3192
automorphism?
homologyAbelianization (H1) = C24×C23 · Schur multiplier (H2) = C24

Aliases

direct productC23×#3251

Subgroups

subgroupG/H
center, socleC22×C23C22×D4
commutator, Frattini, cosocleC2×C4C24×C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 1472

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

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#18594, C23×#18596, C23×#18606, …
maximal normal subgroup ofC23×#18594, C23×#18596, C23×#18606, …
maximal quotient ofC23×#21890, C23×#21891, C23×#21963, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1983);