Finite Group Databasebeta

C22×C4×C8×D11 #15617151

order2816
isoclinismisoclinic class of D11
automorphism?
homologyAbelianization (H1) = C23×C4×C8 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×C4×C8×D11

Splittings

FittingC22×C4×C8×C11 ⋊ C2
derived, SylowC11 ⋊ C23×C4×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4×C8D11
commutator, hypocenterC11C23×C4×C8
FrattiniC2×C4C24×D11
FittingC22×C4×C8×C11C2
socleC24×C11C22×C4
prime radicalC24×D11C2×C4
cosocleC2×C4×C11C25
LCSG ▷ C11
UCSC1 ◁ C22×C4×C8

4638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1032946);