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C23×#1423 #15669042

order2944
nilpotency class5
isoclinismisoclinic class of D32
automorphism?
homologyAbelianization (H1) = C2×C4×C23 · Schur multiplier (H2) = C2

Aliases

direct productC23×#1423

Subgroups

subgroupG/H
center, socle, prime radicalC22×C23D16
commutatorC16C2×C4×C23
Frattini, cosocleC2×C16C22×C23
LCSG ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C2×C4×C23 ◁ C2×C8×C23 ◁ C2×C16×C23 ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 59
transitive degreeμt(G) = 2944

A minimal faithful permutation representation — 2 generators on 59 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)(29,34)(30,35)(31,39)(32,42)(36,51)(37,54)(38,47)(40,56)(41,50)(43,55)(44,45)(46,52)(48,49)(53,59)(57,58);(28,29,35,45,31,36,48,54,42,52,56,59,55,57,41,47,33,38,50,58,43,53,40,46,32,37,49,51,39,44,30,34)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#7537, C23×#7538, C23×#7545, …
maximal normal subgroup ofC23×#7537, C23×#7538, C23×#7545, …
maximal quotient ofC23×#7460, C23×#7471, C23×#7545, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 155);