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C23×#1366 #15668985

order2944
nilpotency class4
isoclinismisoclinic class of #1366
automorphism?
homologyAbelianization (H1) = C2×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×#1366

Subgroups

subgroupG/H
center, socleC2×C23#333
commutatorC42C2×C4×C23
Frattini, cosocleC4×C8C22×C23
prime radicalC22×C23#100
LCSG ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C4×C8×C23 ◁ G

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 55
transitive degreeμt(G) = 736

A minimal faithful permutation representation — 2 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,27,32,40,33,51,49,29,34,42,50,28,31,41,47)(26,35,37,48,43,46,39,54,36,52,53,55,38,30,44,45);(24,26,29,36)(25,30)(27,39,42,44)(28,43,40,38)(31,35)(32,48)(33,52)(34,46)(37,41,53,51)(45,49)(47,54)(50,55)

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C23×#1366, C23×#11956, C23×#11989, …
maximal normal subgroup ofC2×C23×#1366, C23×#11956, C23×#11989, …
maximal quotient ofC23×#7135, C23×#7271, C2×C23×#1366

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 98);