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C22×#19154120 #37551789

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

Aliases

direct productC22×#19154120

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC22#19154120
commutator, cosocle, hypocenterC232C22×C11
FrattiniC1G
Fitting, socleC22×C232C11
LCSG ▷ C232
UCSC1 ◁ C22

260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 2116

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

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, 79);