Finite Group Databasebeta

D47×#2122 #26369007

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

Aliases

direct productD47×#2122

Splittings

FittingC47×#2122 ⋊ C2
SylowC47 ⋊ C2×#2122

Subgroups

subgroupG/H
centerC2C2×#99×D47
commutatorC23×C47C23×C4
FrattiniC2×D4C23×D47
FittingC47×#2122C2
socleC2×C47C22×#99
prime radical#535×D47C2
cosocleC2×D4×C47C24
hypercenter#2122D47
hypocenterC47C2×#2122
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2122

1406 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

575 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322297);