Finite Group Databasebeta

← Prev (#11928780) Next (#11928782) →

C3×#88144 #11928781

order1248
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×#88144

Splittings

HallC3×C13 ⋊ #125
SylowC13 ⋊ C3×#125

Subgroups

subgroupG/H
centerC22×C3C22×D13
commutator, cosocleC22×C13C23×C3
FrattiniC22C22×C3×D13
FittingC3×C13×C4⋊C4C2
socle, prime radicalC22×C3×C13C23
hypercenterC3×C4⋊C4D13
hypocenterC13C3×#125
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 1248

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

Conjugacy classes & character table

222 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 893);