Finite Group Databasebeta

D4×#13093963 #26369486

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productD4×#13093963

Splittings

FittingD4×C16×C47 ⋊ C2
SylowC47 ⋊ D4×M32

Subgroups

subgroupG/H
center, FrattiniC2×C8C23×D47
commutator, socleC22×C47C23×C8
FittingD4×C16×C47C2
prime radicalC2×D4×D47C8
cosocleC2×C8×C47C24
hypercenterD4×C16D47
hypocenterC47D4×M32
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ D4×C16

734 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322776);