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C22×#19154122 #37551791

order23276
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC22×#19154122

Splittings

Fitting, socle, HallC22×C232 ⋊ C11
derived, SylowC232 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC22#19154122
commutator, cosocle, hypocenterC232C22×C11
FrattiniC1G
Fitting, socleC22×C232C11
LCSG ▷ C232
UCSC1 ◁ C22

50 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 1012

A minimal faithful permutation representation — 2 generators on 50 points:

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

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23276, 81);