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C3×#88116 #11928352

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

Aliases

direct productC3×#88116

Splittings

FittingC3×D4×C13 ⋊ C4
HallC3×C13 ⋊ #104
SylowC13 ⋊ C3×#104

Subgroups

subgroupG/H
centerC2×C3C22⋊#261
commutatorC4×C13C2×C3×C4
FrattiniC4C2×C3×#261
FittingC3×D4×C13C4
socleC2×C3×C13C22⋊C4
prime radicalC3×#6129C2
cosocleC4×D13C22×C3
hypercenterC3×D4#261
hypocenterC13C3×#104
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×D4

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 312

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3)(4,5,8,11,15,9,13,14,6,10,16,12,7)(17,19)(18,21)(20,23)(22,24);(5,6,7,9)(8,11,12,16)(10,14,15,13)(17,18,20,22,21,19,24,23)

Conjugacy classes & character table

87 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 464);