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C3×#88106 #11928343

order1248
isoclinismisoclinic class of #6118
automorphism?
homologyAbelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C1

Aliases

direct productC3×#88106

Splittings

HallC3×C13 ⋊ M32
SylowC13 ⋊ C3×M32

Subgroups

subgroupG/H
centerC3×C4C2×#261
commutatorC2×C13C2×C3×C8
FrattiniC4C2×C3×#261
FittingC2×C3×C4×C13C4
socleC2×C3×C13C2×C8
prime radicalC22×C3×C13C8
cosocle#1055C22×C3
hypercenterC2×C3×C4#261
hypocenterC13C3×M32
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C3×C4 ◁ C2×C3×C4

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 624

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 455);