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C23×#1442 #15669061

order2944
nilpotency class2
isoclinismisoclinic class of #392
automorphism?
homologyAbelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C25

Aliases

direct productC23×#1442

Subgroups

subgroupG/H
center, socle, prime radicalC24×C23C23
commutatorC23C22×C4×C23
Frattini, cosocleC24C23×C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 2944

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#7122, C23×#8867, C23×#8869, …
maximal normal subgroup ofC23×#7122, C23×#8867, C23×#8869, …
maximal quotient ofC23×#7556, C23×#7557, C23×#11255, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 174);