Finite Group Databasebeta

C22⋊C4×(C2×D11)⋊C4 #14675173

order2816
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4

Aliases

direct productC22⋊C4×(C2×D11)⋊C4

Splittings

FittingC2×C4×C11×C22⋊C4 ⋊ C2
SylowC11 ⋊ C22⋊C42

Subgroups

subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C22⋊C42
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

4254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 90968);