Finite Group Databasebeta

D47×#2126 #26369054

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

Aliases

direct productD47×#2126

Splittings

FittingC47×#2126 ⋊ C2
SylowC47 ⋊ C2×#2126

Subgroups

subgroupG/H
centerC4#99×D47
commutatorC2×C4×C47C23×C4
FrattiniC2×D4C23×D47
FittingC47×#2126C2
socleC2×C47C22×#99
prime radical#532×D47C2
cosocleC2×D4×C47C24
hypercenter#2126D47
hypocenterC47C2×#2126
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #2126

1338 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, 322344);