Finite Group Databasebeta

Q8×C16×D47 #26369757

order12032
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productQ8×C16×D47

Splittings

FittingQ8×C16×C47 ⋊ C2
SylowC47 ⋊ C2×Q8×C16

Subgroups

subgroupG/H
centerC2×C16C22×D47
commutatorC2×C47C23×C16
FrattiniC2×C8C23×D47
FittingQ8×C16×C47C2
socleC22×C47C23×C8
prime radicalC22×D47C22×C8
cosocleC2×C8×C47C24
hypercenterQ8×C16D47
hypocenterC47C2×Q8×C16
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C16 ◁ Q8×C16

582 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, 323047);