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C23×#1380 #15668999

order2944
nilpotency class4
isoclinismisoclinic class of D16
automorphism?
homologyAbelianization (H1) = C42×C23 · Schur multiplier (H2) = C23

Aliases

direct productC23×#1380

Subgroups

subgroupG/H
center, socle, prime radicalC23×C23D8
commutatorC8C42×C23
Frattini, cosocleC22×C8C22×C23
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C22×C4×C23 ◁ C22×C8×C23 ◁ G

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 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)(26,27)(28,29,30,31)(33,38)(34,42)(35,44)(36,43)(39,40)(41,47)(45,46);(25,27)(32,33,35,39,36,40,34,38,37,41,42,46,43,45,44,47)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#7418, C23×#7419, C2×C23×#1380, …
maximal normal subgroup ofC23×#7418, C23×#7419, C2×C23×#1380, …
maximal quotient ofC23×#7154, C23×#7171, C23×#7217, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 112);