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C3×#88068 #11928058

order1248
isoclinismisoclinic class of #88066
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×#88068

Splittings

FittingC3×C13×Q16 ⋊ C2
HallC3×C13 ⋊ SD32
SylowC13 ⋊ C3×SD32

Subgroups

subgroupG/H
centerC2×C3#6104
commutator, cosocleC8×C13C22×C3
FrattiniC8C2×C3×D13
FittingC3×C13×Q16C2
socleC2×C3×C13D8
prime radicalC3×D104C2
hypercenterC3×Q16D13
hypocenterC13C3×SD32
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×Q16

52 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)(4,5,7,9,11,13,15,16,14,12,10,8,6)(17,18,21,24)(19,26,28,32)(20,29,27,23)(22,30,31,25);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(18,22)(19,25)(20,27)(23,32)(24,31)(26,29)(28,30)

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 170);