Finite Group Databasebeta

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C3×#88067 #11928057

order1248
isoclinismisoclinic class of #88066
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×#88067

Splittings

HallC3×C13 ⋊ SD32
SylowC13 ⋊ C3×SD32

Subgroups

subgroupG/H
centerC2×C3#6104
commutator, cosocleC8×C13C22×C3
FrattiniC8C2×C3×D13
Fitting, prime radicalC3×C13×D8C2
socleC2×C3×C13D8
hypercenterC3×D8D13
hypocenterC13C3×SD32
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×D8

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

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 169);