Finite Group Databasebeta

D47×#2089 #26245385

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

Aliases

direct productD47×#2089

Splittings

FittingC47×#2089 ⋊ C2
SylowC47 ⋊ C2×#2089

Subgroups

subgroupG/H
centerC22#121×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2089C2
socleC22×C47C2×#121
prime radicalC23×D47#41
hypercenter#2089D47
hypocenterC47C2×#2089
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2089

810 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

650 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 198675);