Finite Group Databasebeta

Q32×C22⋊D47 #26373002

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

Aliases

direct productQ32×C22⋊D47

Splittings

FittingC22×Q32×C47 ⋊ C2
SylowC47 ⋊ D4×Q32

Subgroups

subgroupG/H
centerC22C2×D8×D47
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC22×Q32×C47C2
socleC22×C47C22×D8
prime radicalC2×C22⋊D47D8
hypercenterC22×Q32D47
hypocenterC47D4×Q32
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q32

664 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1067 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 326292);