Finite Group Databasebeta

D4×Dic376 #26373008

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

Aliases

direct productD4×Dic376

Splittings

SylowC47 ⋊ D4×Q32

Subgroups

subgroupG/H
centerC22C22×D376
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingD4×C16×C47C2
socleC22×C47C22×D8
prime radicalC2×D4×C47D8
hypercenterD4×C16D47
hypocenterC47D4×Q32
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×C16

664 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1895 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 326298);