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C3×#88254 #11929279

order1248
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productC3×#88254

Splittings

FittingC2×C3×Q8×C13 ⋊ C2
HallC3×C13 ⋊ 2−1+4
SylowC13 ⋊ C3×2−1+4

Subgroups

subgroupG/H
centerC2×C3C23×D13
commutator, cosocleC2×C13C24×C3
FrattiniC2C23×C3×D13
FittingC2×C3×Q8×C13C2
socleC2×C3×C13C24
hypercenterC2×C3×Q8D13
hypocenterC13C3×2−1+4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C2×C3×Q8

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 32 points:

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

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1391);