Finite Group Databasebeta

D4×#13063269 #25253267

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD4×#13063269

Splittings

SylowC43 ⋊ D4×SD32

Subgroups

subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
Fitting, prime radicalD4×D8×C43C2
socleC22×C43C22×D8
hypercenterD4×D8D43
hypocenterC43D4×SD32
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×D8

738 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

790 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 326238);