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C3×#88062 #11928052

order1248
isoclinismisoclinic class of #6104
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#88062

Splittings

HallC3×C13 ⋊ #108
SylowC13 ⋊ C3×#108

Subgroups

subgroupG/H
centerC3×C4C22⋊D13
commutatorC4×C13C2×C3×C4
FrattiniC2×C4C2×C3×D13
FittingC3×C13×M16C2
socleC2×C3×C13C4⋊C4
prime radicalC22×C3×C13Q8
cosocleC2×C4×C13C22×C3
hypercenterC3×M16D13
hypocenterC13C3×#108
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×M16

60 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)(4,5,7,9,11,13,15,16,14,12,10,8,6)(17,19,20,28,22,29,21,30)(18,23,24,27,26,31,25,32);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,21,25,22,26,20,24)(19,27,28,31,29,32,30,23)

Conjugacy classes & character table

222 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 164);