Finite Group Databasebeta

D4×C16×D47 #26369424

order12032
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productD4×C16×D47

Splittings

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

Subgroups

subgroupG/H
centerC2×C16C22×D47
commutatorC2×C47C23×C16
FrattiniC2×C8C23×D47
FittingD4×C16×C47C2
socleC22×C47C23×C8
prime radicalC2×D4×D47C8
cosocleC2×C8×C47C24
hypercenterD4×C16D47
hypocenterC47C2×D4×C16
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C16 ◁ D4×C16

806 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322714);