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C3×#88173 #11928809

order1248
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC3×#88173

Splittings

FittingC3×C13×Q16 ⋊ C2
HallC3×C13 ⋊ #135
SylowC13 ⋊ C3×#135

Subgroups

subgroupG/H
centerC2×C3D4×D13
commutator, cosocleC4×C13C23×C3
FrattiniC4C22×C3×D13
FittingC3×C13×Q16C2
socleC2×C3×C13C2×D4
hypercenterC3×Q16D13
hypocenterC13C3×#135
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×Q16

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 921);