Finite Group Databasebeta

C22×(C22⋊D11)⋊C8 #15617602

order2816
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC22×(C22⋊D11)⋊C8

Splittings

FittingC22×C11×C22⋊C8 ⋊ C2
SylowC11 ⋊ C22×C8×D4

Subgroups

subgroupG/H
centerC23×C4C22×D11
commutatorC2×C11C24×C8
FrattiniC2×C4C24×D11
FittingC22×C11×C22⋊C8C2
socleC24×C11C22×C4
prime radicalC23×C22⋊D11C4
cosocleC2×C4×C11C25
hypercenterC22×C22⋊C8D11
hypocenterC11C22×C8×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

3694 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, 1033397);