Finite Group Databasebeta

D47×#2000 #26243064

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productD47×#2000

Splittings

FittingC47×#2000 ⋊ C2
SylowC47 ⋊ C2×#2000

Subgroups

subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2000C2
socleC23×C47C22×D4
prime radicalC2×#121×D47C2
hypercenter#2000D47
hypocenterC47C2×#2000
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

2526 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, 196354);