Finite Group Databasebeta

D47×#2086 #26245314

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

Aliases

direct productD47×#2086

Splittings

FittingC47×#2086 ⋊ C2
SylowC47 ⋊ C2×#2086

Subgroups

subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2086C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenter#2086D47
hypocenterC47C2×#2086
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2086

1054 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, 198604);