Finite Group Databasebeta

D47×#2176 #26369571

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD47×#2176

Splittings

FittingC47×#2176 ⋊ C2
SylowC47 ⋊ C2×#2176

Subgroups

subgroupG/H
centerC22C2×D8×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC47×#2176C2
socleC22×C47C22×D8
prime radicalC22×D47C2×D8
cosocleC2×C8×C47C24
hypercenter#2176D47
hypocenterC47C2×#2176
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2176

670 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

800 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322861);