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C3×#88198 #11928832

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

Aliases

direct productC3×#88198

Splittings

HallC3×C13 ⋊ C4⋊Q8
SylowC13 ⋊ C3×C4⋊Q8

Subgroups

subgroupG/H
centerC22×C3C22×D13
commutator, cosocleC22×C13C23×C3
FrattiniC22C22×C3×D13
FittingC2×C3×Q8×C13C2
socle, prime radicalC22×C3×C13C23
hypercenterC2×C3×Q8D13
hypocenterC13C3×C4⋊Q8
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C3 ◁ C2×C3×Q8

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 1248

A minimal faithful permutation representation — 3 generators on 28 points:

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

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, 944);