Finite Group Databasebeta

D4×#13093970 #26373004

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD4×#13093970

Splittings

SylowC47 ⋊ D4×Q32

Subgroups

subgroupG/H
centerC22C22×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingD4×Q16×C47C2
socleC22×C47C22×D8
prime radicalC2×D4×C47D8
hypercenterD4×Q16D47
hypocenterC47D4×Q32
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×Q16

664 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

860 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 326294);