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C2×C23×#494 #15670764

order2944
nilpotency class3
isoclinismisoclinic class of #465
automorphism?
homologyAbelianization (H1) = C24×C23 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C23×#494

Subgroups

subgroupG/H
center, socle, prime radicalC23×C23C2×D4
commutator, Frattini, cosocleC2×C4C24×C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G

552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 2944

A minimal faithful permutation representation — 4 generators on 45 points:

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

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#9066, C23×#9733, C23×#9742, …
maximal normal subgroup ofC23×#9066, C23×#9733, C23×#9742, …
maximal quotient ofC2×C23×#1707, C2×C23×#1710, C2×C23×#1713, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1877);