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C13×#824 #11928095

order1248
automorphism?
homologyAbelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×#824

Splittings

HallC3×C13 ⋊ #101
SylowC3 ⋊ C13×#101

Subgroups

subgroupG/H
centerC2×C13(C2×D3)⋊C4
commutatorC22×C3C2×C4×C13
FrattiniC2×C4C2×D3×C13
FittingC3×C13×M16C2
socleC2×C3×C13C22⋊C4
prime radicalC22×C3×C13C2×C4
cosocleC2×C3×C4C22×C13
hypercenterC13×M16D3
hypocenterC3C13×#101
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C13×M16

76 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)(17,19,20,26,21,27,29,32)(18,22,23,30,24,25,28,31);(15,16)(17,18,21,24)(19,25,27,22)(20,28,29,23)(26,30,32,31)

Conjugacy classes & character table

273 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 207);