Finite Group Databasebeta

D47×#1681 #26198567

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD47×#1681

Splittings

FittingC47×#1681 ⋊ C2
SylowC47 ⋊ C2×#1681

Subgroups

subgroupG/H
centerC22#121×D47
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC47×#1681C2
socleC22×C47C2×#121
prime radical#459×D47C2
hypercenter#1681D47
hypocenterC47C2×#1681
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #1681

842 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

725 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 151857);