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C23×#2069 #15669688

order2944
nilpotency class3
isoclinismisoclinic class of #2069
automorphism?
homologyAbelianization (H1) = C23×C23 · Schur multiplier (H2) = C22

Aliases

direct productC23×#2069

Subgroups

subgroupG/H
center, socleC2×C23#396
commutator, Frattini, cosocleC22×C4C23×C23
prime radicalC22×D4×C23C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C23 ◁ C22×C4×C23 ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(24,25,29,31,28,32,27,36)(26,33,37,38,34,39,35,30);(24,26,27,35,28,34,29,37)(25,30,31,33,32,38,36,39);(26,34)(27,29)(31,36)(33,39)

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C23×#2069, C23×#23622, C23×#24808, …
maximal normal subgroup ofC2×C23×#2069, C23×#23622, C23×#24808, …
maximal quotient ofC23×#10603, C23×#10605, C23×#10607, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 801);