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C3×#88103 #11928340

order1248
isoclinismisoclinic class of #88101
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#88103

Splittings

HallC3×C13 ⋊ #108
SylowC13 ⋊ C3×#108

Subgroups

subgroupG/H
centerC2×C3C4⋊#261
commutatorC4×C13C2×C3×C4
FrattiniC4C2×C3×#261
FittingC3×C8×C13C4
socleC2×C3×C13C4⋊C4
prime radicalC2×C3×D13Q8
cosocleC4×D13C22×C3
hypercenterC3×C8#261
hypocenterC13C3×#108
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8

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

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 452);