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C23×#2433 #15670052

order2944
nilpotency class2
isoclinismisoclinic class of #2403
automorphism?
homologyAbelianization (H1) = C24×C23 · Schur multiplier (H2) = C26×C4

Aliases

direct productC23×#2433

Subgroups

subgroupG/H
center, socleC23×C23C24
commutator, Frattini, cosocleC23C24×C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C23 ◁ G

1348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 736

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#9463, C23×#9946, C23×#9954, …
maximal normal subgroup ofC23×#9463, C23×#9946, C23×#9954, …
maximal quotient ofC23×#13880, C23×#13902, C23×#13977, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1165);