Finite Group Databasebeta

D4×#66900 #14769143

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

Aliases

direct productD4×#66900

Splittings

SylowC11 ⋊ D4×#101

Subgroups

subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×D4×Q8×C11C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC2×D4×Q8D11
hypocenterC11D4×#101
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×D4×Q8

1378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 184938);