Finite Group Databasebeta

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C23×#3542 #15671161

order2944
nilpotency class2
isoclinismisoclinic class of #3532
automorphism?
homologyAbelianization (H1) = C25×C23 · Schur multiplier (H2) = C28

Aliases

direct productC23×#3542

Subgroups

subgroupG/H
center, socleC22×C23C25
commutator, Frattini, cosocleC22C25×C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C23 ◁ G

1160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 5 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)(24,25,28,26)(27,30,31,29)(33,36)(34,38);(25,26)(29,30)(33,36)(37,39);(32,33)(34,37)(35,36)(38,39);(24,26,28,25)(27,30,31,29)(32,34)(33,37)(35,38)(36,39);(24,27,28,31)(25,29,26,30)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#61609, C23×#61611, C23×#61614, …
maximal normal subgroup ofC23×#61609, C23×#61611, C23×#61614, …
maximal quotient ofC23×#34362, C23×#34363, C23×#34404, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2274);