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C13×#827 #11928098

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

Aliases

direct productC13×#827

Splittings

HallC3×C13 ⋊ SD32
SylowC3 ⋊ C13×SD32

Subgroups

subgroupG/H
centerC2×C13#213
commutator, cosocleC3×C8C22×C13
FrattiniC8C2×D3×C13
Fitting, prime radicalC3×C13×D8C2
socleC2×C3×C13D8
hypercenterC13×D8D3
hypocenterC3C13×SD32
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C13 ◁ C4×C13 ◁ C8×C13 ◁ C13×D8

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:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16)(18,22)(19,26)(20,27)(23,24)(25,31)(28,32)(29,30);(15,16)(17,18,21,25)(19,22,28,31)(20,29,27,24)(23,32,30,26)

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, 210);