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C23×#3217 #15670836

order2944
nilpotency class3
isoclinismisoclinic class of #3192
automorphism?
homologyAbelianization (H1) = C24×C23 · Schur multiplier (H2) = C23×C4

Aliases

direct productC23×#3217

Subgroups

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

490 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)(34,36)(35,37)(38,39);(24,26,27,31)(25,28,29,30)(33,36)(37,38);(26,31)(28,30)(33,37)(35,39)(36,38);(25,29)(28,30)(33,36)(37,38)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#9340, C23×#9378, C23×#18335, …
maximal normal subgroup ofC23×#9340, C23×#9378, C23×#18335, …
maximal quotient ofC23×#21810, C23×#21867, C23×#21987, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1949);