Finite Group Databasebeta

C2×(C22⋊D11)⋊C16 #14906920

order2816
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productC2×(C22⋊D11)⋊C16

Splittings

FittingC2×C11×C22⋊C16 ⋊ C2
SylowC11 ⋊ C2×D4×C16

Subgroups

subgroupG/H
centerC22×C8C22×D11
commutatorC2×C11C23×C16
FrattiniC2×C8C23×D11
FittingC2×C11×C22⋊C16C2
socleC23×C11C22×C8
prime radicalC22×C22⋊D11C8
cosocleC2×C8×C11C24
hypercenterC2×C22⋊C16D11
hypocenterC11C2×D4×C16
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C8 ◁ C2×C22⋊C16

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 322715);