Finite Group Databasebeta

C22×D11×C22⋊Q8 #15660412

order2816
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×D11×C22⋊Q8

Splittings

FittingC22×C11×C22⋊Q8 ⋊ C2
SylowC11 ⋊ C23×C22⋊Q8

Subgroups

subgroupG/H
centerC24C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC22×C22⋊Q8D11
hypocenterC11C23×C22⋊Q8
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

14078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1076207);