Finite Group Databasebeta

← Prev (#11928041) Next (#11928043) →

C3×#88052 #11928042

order1248
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C1

Aliases

direct productC3×#88052

Splittings

HallC3×C13 ⋊ M32
SylowC13 ⋊ C3×M32

Subgroups

subgroupG/H
centerC3×C8C2×D13
commutatorC2×C13C2×C3×C8
FrattiniC8C2×C3×D13
FittingC2×C3×C8×C13C2
socleC2×C3×C13C2×C8
prime radicalC22×C3×C13C8
cosocleC8×C13C22×C3
hypercenterC2×C3×C8D13
hypocenterC13C3×M32
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C3×C8 ◁ C2×C3×C8

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

348 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 154);