Finite Group Databasebeta

C4×D4×C11⋊C8 #14752087

order2816
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×D4×C11⋊C8

Splittings

SylowC11 ⋊ C4×C8×D4

Subgroups

subgroupG/H
centerC2×C42C22×D11
commutatorC2×C11C22×C4×C8
FrattiniC22×C4C23×D11
FittingC42×D4×C11C2
socleC23×C11C23×C4
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC42×D4D11
hypocenterC11C4×C8×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C42 ◁ C42×D4

1422 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, 167882);