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C23×#3068 #15670687

order2944
nilpotency class3
isoclinismisoclinic class of #3068
automorphism?
homologyAbelianization (H1) = C24×C23 · Schur multiplier (H2) = C25

Aliases

direct productC23×#3068

Subgroups

subgroupG/H
center, socleC2×C23C2×#121
commutator, Frattini, cosocleC2×C4C24×C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C23 ◁ C22×C4×C23 ◁ G

466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 368

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

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#24420, C23×#24422, C23×#24472, …
maximal normal subgroup ofC23×#24420, C23×#24422, C23×#24472, …
maximal quotient ofC23×#19162, C23×#19165, C23×#19166, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1800);