Finite Group Databasebeta

← Prev (#10587258) Next (#10587260) →

C3×#4339 #10587259

order528
isoclinismisoclinic class of Dic22
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC3×#4339

Splittings

FittingC2×C3×C4×C11 ⋊ C2
HallC3×C11 ⋊ #41
SylowC11 ⋊ C3×#41

Subgroups

subgroupG/H
centerC3×C4C2×D11
commutator, cosocleC2×C11C23×C3
FrattiniC2C22×C3×D11
FittingC2×C3×C4×C11C2
socleC2×C3×C11C23
hypercenterC2×C3×C4D11
hypocenterC11C3×#41
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C3×C4 ◁ C2×C3×C4

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 264

A minimal faithful permutation representation — 3 generators on 22 points:

(1,2,3)(4,5,7,9,11,13,14,12,10,8,6)(16,20)(19,22);(15,17,18,21)(16,19,20,22);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,19)(18,20)(21,22)

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11760513, #11760514, C3×#66869, …
maximal normal subgroup of#11760513, #11760514, C3×#66869, …
maximal quotient ofC3×C4×Dic22, C3×#66923, C3×#66925, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 129);