Finite Group Databasebeta

C2×C11×D12 #10587268

order528
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C23×C11 · Schur multiplier (H2) = C23

Aliases

direct productC2×C11×D12

Splittings

FittingC2×C3×C4×C11 ⋊ C2
HallC3×C11 ⋊ C2×D4
SylowC3 ⋊ C2×D4×C11

Subgroups

subgroupG/H
centerC22×C11C2×D3
commutator, cosocleC2×C3C23×C11
FrattiniC2C22×D3×C11
FittingC2×C3×C4×C11C2
socleC22×C3×C11C22
hypercenterC2×C4×C11D3
hypocenterC3C2×D4×C11
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C11 ◁ C2×C4×C11

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 264

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11760496, #11760503, #11760504, …
maximal normal subgroup of#11760496, #11760503, #11760504, …
maximal quotient ofC11×#869, C4×C11×D12, C11×#874, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 138);