Finite Group Databasebeta

D4×#66889 #14769441

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#66889

Splittings

FittingD4×C11×M16 ⋊ C2
SylowC11 ⋊ D4×#104

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×M16C2
socleC22×C11C22×C22⋊C4
prime radicalD4×#4339C2
cosocleC22×C4×C11C24
hypercenterD4×M16D11
hypocenterC11D4×#104
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×M16

1608 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 185236);