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C23×#2254 #15669873

order2944
nilpotency class4
isoclinismisoclinic class of #2215
automorphism?
homologyAbelianization (H1) = C23×C23 · Schur multiplier (H2) = C4

Aliases

direct productC23×#2254

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

128 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)(34,41)(35,42)(38,43)(39,47)(40,46)(44,45);(24,26,27,31)(25,28,29,30);(32,33,38,47,35,39,34,37,36,40,41,45,42,44,43,46)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#7453, C23×#12394, C23×#12395, …
maximal normal subgroup ofC23×#7453, C23×#12394, C23×#12395, …
maximal quotient ofC23×#12906, C23×#13166, C23×#13282, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 986);