Finite Group Databasebeta

D4×D688 #25253252

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD4×D688

Splittings

FittingD4×C16×C43 ⋊ C2
SylowC43 ⋊ D4×D16

Subgroups

subgroupG/H
centerC22C22×D344
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingD4×C16×C43C2
socleC22×C43C22×D8
hypercenterD4×C16D43
hypocenterC43D4×D16
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×C16

812 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1735 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 326223);