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C4×#19154123 #37551748

order23276
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC4×#19154123

Splittings

Fitting, HallC4×C232 ⋊ C11
derived, SylowC232 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC4#19154123
commutator, hypocenterC232C4×C11
FrattiniC2C2×#19154123
FittingC4×C232C11
socle, cosocleC2×C232C2×C11
prime radicalC2×#19154123C2
LCSG ▷ C232
UCSC1 ◁ C4

30 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:

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

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, 38);