Finite Group Databasebeta

← Prev (#11929174) Next (#11929176) →

C3×#88240 #11929175

order1248
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×#88240

Splittings

HallC3×C13 ⋊ #131
SylowC13 ⋊ C3×#131

Subgroups

subgroupG/H
centerC2×C3C22×#261
commutatorC2×C13C22×C3×C4
FrattiniC2C22×C3×#261
FittingC3×Q8×C13C4
socleC2×C3×C13C22×C4
prime radicalC3×#6131C2
cosocleDic13C23×C3
hypercenterC3×Q8#261
hypocenterC13C3×#131
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C3×Q8

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

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1287);