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C13×#829 #11928100

order1248
isoclinismisoclinic class of #826
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×#829

Splittings

HallC3×C13 ⋊ Q32
SylowC3 ⋊ C13×Q32

Subgroups

subgroupG/H
centerC2×C13#213
commutator, cosocleC3×C8C22×C13
FrattiniC8C2×D3×C13
FittingC3×C13×Q16C2
socle, prime radicalC2×C3×C13D8
hypercenterC13×Q16D3
hypocenterC3C13×Q32
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C13 ◁ C4×C13 ◁ C8×C13 ◁ C13×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:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16)(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);(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

234 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 212);