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C23×#2255 #15669874

order2944
nilpotency class4
isoclinismisoclinic class of #2218
automorphism?
homologyAbelianization (H1) = C23×C23 · Schur multiplier (H2) = C2

Aliases

direct productC23×#2255

Subgroups

subgroupG/H
center, socle, prime radicalC22×C23C2×D8
commutator, Frattini, cosocleC2×C8C23×C23
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C42×C23 ◁ C4×C8×C23 ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 2944

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)(24,25,27,29)(26,30,31,28)(33,37)(34,39)(35,41)(38,43)(40,47)(42,46)(44,45);(24,26,27,31)(25,28,29,30)(33,38)(37,43)(40,44)(45,47);(32,33,39,45,35,40,42,43,36,38,46,47,41,44,34,37)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#12400, C23×#12401, C23×#12402, …
maximal normal subgroup ofC23×#12400, C23×#12401, C23×#12402, …
maximal quotient ofC23×#12908, C23×#13167, C23×#13168, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 987);