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C3×#88166 #11928802

order1248
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC3×#88166

Splittings

FittingC3×C13×D8 ⋊ C2
HallC3×C13 ⋊ #135
SylowC13 ⋊ C3×#135

Subgroups

subgroupG/H
centerC2×C3D4×D13
commutator, cosocleC4×C13C23×C3
FrattiniC4C22×C3×D13
FittingC3×C13×D8C2
socleC2×C3×C13C2×D4
hypercenterC3×D8D13
hypocenterC13C3×#135
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×D8

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 914);