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C13×#1007 #11929294

order1248
automorphism?
homologyAbelianization (H1) = C24×C13 · Schur multiplier (H2) = C25

Aliases

direct productC13×#1007

Splittings

FittingC2×C3×Q8×C13 ⋊ C2
HallC3×C13 ⋊ 2−1+4
SylowC3 ⋊ C13×2−1+4

Subgroups

subgroupG/H
centerC2×C13C23×D3
commutator, cosocleC2×C3C24×C13
FrattiniC2C23×D3×C13
FittingC2×C3×Q8×C13C2
socleC2×C3×C13C24
hypercenterC2×Q8×C13D3
hypocenterC3C13×2−1+4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C13 ◁ C2×Q8×C13

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 624

A minimal faithful permutation representation — 4 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1406);