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C3×#88113 #11928350

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

Aliases

direct productC3×#88113

Splittings

HallC3×C13 ⋊ #101
SylowC13 ⋊ C3×#101

Subgroups

subgroupG/H
centerC2×C3C22⋊#261
commutatorC22×C13C2×C3×C4
FrattiniC22C2×C3×#261
FittingC2×C3×C4×C13C4
socleC2×C3×C13C22⋊C4
prime radicalC22×C3×C13C2×C4
cosocleC2×Dic13C22×C3
hypercenterC2×C3×C4#261
hypocenterC13C3×#101
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×C4

76 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)(4,5,8,11,15,9,13,14,6,10,16,12,7)(17,19,21,27)(18,22,24,25)(20,28,29,26)(23,31,32,30);(5,6,7,9)(8,11,12,16)(10,14,15,13)(17,18,20,23,21,24,29,32)(19,25,26,31,27,22,28,30)

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 462);