Finite Group Databasebeta

Q32×C22⋊D11 #14910497

order2816
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productQ32×C22⋊D11

Splittings

FittingC22×C11×Q32 ⋊ C2
SylowC11 ⋊ D4×Q32

Subgroups

subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC22×C11×Q32C2
socleC22×C11C22×D8
prime radicalC2×C22⋊D11D8
hypercenterC22×Q32D11
hypocenterC11D4×Q32
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q32

664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 326292);