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C3×#88101 #11928338

order1248
isoclinismisoclinic class of #88101
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×#88101

Splittings

FittingC3×C8×C13 ⋊ C4
HallC3×C13 ⋊ #106
SylowC13 ⋊ C3×#106

Subgroups

subgroupG/H
centerC2×C3C4⋊#261
commutatorC4×C13C2×C3×C4
FrattiniC4C2×C3×#261
FittingC3×C8×C13C4
socleC2×C3×C13C4⋊C4
prime radicalC2×C3×D13D4
cosocleC4×D13C22×C3
hypercenterC3×C8#261
hypocenterC13C3×#106
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8

72 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)(17,18,19,21,20,22,23,24);(5,6,7,9)(8,11,12,16)(10,14,15,13)(18,21)(19,23)(22,24)

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 450);