Finite Group Databasebeta

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C3×#88131 #11928767

order1248
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×#88131

Splittings

HallC3×C13 ⋊ #117
SylowC13 ⋊ C3×#117

Subgroups

subgroupG/H
centerC22×C3C22×D13
commutatorC2×C13C22×C3×C4
FrattiniC22C22×C3×D13
FittingC3×C13×C22⋊C4C2
socleC22×C3×C13C23
prime radicalC23×C3×C13C22
cosocleC22×C13C23×C3
hypercenterC3×C22⋊C4D13
hypocenterC13C3×#117
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C3 ◁ C3×C22⋊C4

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 624

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)(17,18,19,20)(23,27)(25,28);(21,23)(22,25)(24,27)(26,28);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(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, 879);