Finite Group Databasebeta

D47×#1976 #26220248

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

Aliases

direct productD47×#1976

Splittings

FittingC47×#1976 ⋊ C2
SylowC47 ⋊ C2×#1976

Subgroups

subgroupG/H
centerC4#121×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1976C2
socleC2×C47C2×#390
prime radicalC2×#135×D47C2
cosocleC22×C4×C47C24
hypercenter#1976D47
hypocenterC47C2×#1976
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1976

1474 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, 173538);