Finite Group Databasebeta

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C23×#3488 #15671107

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

Aliases

direct productC23×#3488

Subgroups

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

1658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 736

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);(28,30,31,35)(29,33,32,34)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#8465, C23×#17603, C23×#17611, …
maximal normal subgroup ofC23×#8465, C23×#17603, C23×#17611, …
maximal quotient ofC23×#34175, C23×#34202, C23×#34204, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2220);