Finite Group Databasebeta

← Prev (#11760564) Next (#11760566) →

C3×#66890 #11760565

order1056
isoclinismisoclinic class of #66890
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×#66890

Splittings

FittingC3×C11×D8 ⋊ C2
HallC3×C11 ⋊ D16
SylowC11 ⋊ C3×D16

Subgroups

subgroupG/H
centerC2×C3#4323
commutator, cosocleC8×C11C22×C3
FrattiniC8C2×C3×D11
FittingC3×C11×D8C2
socleC2×C3×C11D8
hypercenterC3×D8D11
hypocenterC11C3×D16
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×D8

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 528

A minimal faithful permutation representation — 2 generators on 30 points:

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

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1056, 102);