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C23×#1558 #15669177

order2944
nilpotency class3
isoclinismisoclinic class of #1510
automorphism?
homologyAbelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C23

Aliases

direct productC23×#1558

Subgroups

subgroupG/H
center, socleC22×C23C2×C22⋊C4
commutatorC2×C4C22×C4×C23
Frattini, cosocleC42C23×C23
prime radicalC23×C23C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 1472

A minimal faithful permutation representation — 3 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,29,27,28,30,31)(32,33)(34,40)(35,43)(36,38)(37,41)(39,45)(42,47)(44,46);(25,28)(26,30)(32,34,36,42)(33,37,38,46)(35,44,45,41)(39,47,43,40);(33,38)(37,46)(39,43)(40,47)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#7483, C23×#8498, C23×#8524, …
maximal normal subgroup ofC23×#7483, C23×#8498, C23×#8524, …
maximal quotient ofC23×#7595, C23×#7605, C23×#7629, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 290);