Finite Group Databasebeta

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C23×#3492 #15671111

order2944
nilpotency class2
isoclinismisoclinic class of #3484
automorphism?
homologyAbelianization (H1) = C25×C23 · Schur multiplier (H2) = C28

Aliases

direct productC23×#3492

Subgroups

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

1124 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)(26,27)(28,29)(30,31)(34,38)(36,39);(25,29)(26,30)(32,33,35,37)(34,36,38,39);(32,34)(33,36)(35,38)(37,39);(24,26,28,30)(25,27,29,31);(24,27)(25,30)(26,29)(28,31)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#8347, C23×#8454, C23×#18164, …
maximal normal subgroup ofC23×#8347, C23×#8454, C23×#18164, …
maximal quotient ofC23×#34178, C23×#34200, C23×#34218, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2224);