Finite Group Databasebeta

D47×#2040 #26243915

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD47×#2040

Splittings

FittingC47×#2040 ⋊ C2
SylowC47 ⋊ C2×#2040

Subgroups

subgroupG/H
centerC22#120×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2040C2
socleC22×C47C2×#120
prime radical#537×D47C2
hypercenter#2040D47
hypocenterC47C2×#2040
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2040

1498 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, 197205);