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C3×#88141 #11928777

order1248
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×#88141

Splittings

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

Subgroups

subgroupG/H
centerC22×C3C22×D13
commutatorC2×C13C22×C3×C4
FrattiniC22C22×C3×D13
FittingC3×C13×C4⋊C4C2
socle, prime radicalC22×C3×C13C23
cosocleC22×C13C23×C3
hypercenterC3×C4⋊C4D13
hypocenterC13C3×C4×Q8
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

140 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)(17,19,20,18)(23,27)(25,28);(21,23,24,27)(22,25,26,28);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,20,19)(21,22,24,26)(23,25,27,28)

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 889);