Finite Group Databasebeta

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C23×#3484 #15671103

order2944
nilpotency class2
isoclinismisoclinic class of #3484
automorphism?
homologyAbelianization (H1) = C25×C23 · Schur multiplier (H2) = C29

Aliases

direct productC23×#3484

Subgroups

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

1900 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 368

A minimal faithful permutation representation — 5 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,27)(28,29)(30,34)(31,32)(33,35);(29,32)(33,34);(24,25)(26,27);(28,29)(30,33)(31,32)(34,35);(28,30)(29,33)(31,35)(32,34)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#8453, C23×#8534, C23×#12705, …
maximal normal subgroup ofC23×#8453, C23×#8534, C23×#12705, …
maximal quotient ofC23×#34171, C23×#34198, C23×#34200, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2216);