Finite Group Databasebeta

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C3×#88202 #11928838

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

Aliases

direct productC3×#88202

Splittings

HallC3×C13 ⋊ #131
SylowC13 ⋊ C3×#131

Subgroups

subgroupG/H
centerC3×C4C22×D13
commutatorC2×C13C22×C3×C4
FrattiniC4C22×C3×D13
Fitting, prime radicalC3×C13×#41C2
socleC2×C3×C13C22×C4
cosocleC4×C13C23×C3
hypercenterC3×#41D13
hypocenterC13C3×#131
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C3×C4 ◁ C3×#41

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

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, 950);