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C3×#88069 #11928059

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

Aliases

direct productC3×#88069

Splittings

HallC3×C13 ⋊ Q32
SylowC13 ⋊ C3×Q32

Subgroups

subgroupG/H
centerC2×C3#6104
commutator, cosocleC8×C13C22×C3
FrattiniC8C2×C3×D13
FittingC3×C13×Q16C2
socle, prime radicalC2×C3×C13D8
hypercenterC3×Q16D13
hypocenterC13C3×Q32
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×Q16

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 1248

A minimal faithful permutation representation — 2 generators on 48 points:

(1,2,3)(4,5,7,9,11,13,15,16,14,12,10,8,6)(17,19,22,30)(18,23,26,40)(20,32,35,48)(21,37,33,29)(24,42,43,47)(25,44,36,39)(27,45,46,31)(28,41,38,34);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,22,26)(19,27,30,46)(20,31,35,45)(21,36,33,25)(23,38,40,28)(24,41,43,34)(29,47,37,42)(32,44,48,39)

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, 171);