Finite Group Databasebeta

D47×#1524 #26184158

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

Aliases

direct productD47×#1524

Splittings

FittingC47×#1524 ⋊ C2
SylowC47 ⋊ C2×#1524

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1524C2
socleC22×C47C22×C22⋊C4
prime radical#121×D47C4
cosocleC42×C47C24
hypercenter#1524D47
hypocenterC47C2×#1524
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1524

1166 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 137448);