Finite Group Databasebeta

D47×Q128 #26137326

order12032
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productD47×Q128

Splittings

FittingC47×Q128 ⋊ C2
SylowC47 ⋊ C2×Q128

Subgroups

subgroupG/H
centerC2D32×D47
commutator, cosocleC32×C47C23
FrattiniC32C22×D47
FittingC47×Q128C2
socleC2×C47C2×D32
prime radicalC2×D47D32
hypercenterQ128D47
hypocenterC47C2×Q128
LCSG ▷ C32×C47 ▷ C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ Q128

126 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

875 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 90616);