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C3×#88238 #11929173

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

Aliases

direct productC3×#88238

Splittings

HallC3×C13 ⋊ #131
SylowC13 ⋊ C3×#131

Subgroups

subgroupG/H
centerC2×C3C22×#261
commutatorC2×C13C22×C3×C4
FrattiniC2C22×C3×#261
FittingC3×D4×C13C4
socleC2×C3×C13C22×C4
prime radicalC3×#6129C2
cosocleDic13C23×C3
hypercenterC3×D4#261
hypocenterC13C3×#131
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C3×D4

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 32 points:

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

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, 1285);