Finite Group Databasebeta

← Prev (#11928796) Next (#11928798) →

C3×#88161 #11928797

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

Aliases

direct productC3×#88161

Splittings

FittingC3×C13×M16 ⋊ C2
HallC3×C13 ⋊ #131
SylowC13 ⋊ C3×#131

Subgroups

subgroupG/H
centerC3×C4C22×D13
commutatorC2×C13C22×C3×C4
FrattiniC4C22×C3×D13
FittingC3×C13×M16C2
socleC2×C3×C13C22×C4
prime radicalC3×#6127C2
cosocleC4×C13C23×C3
hypercenterC3×M16D13
hypocenterC13C3×#131
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C3×C4 ◁ C3×M16

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 909);