Finite Group Databasebeta

D47×#1721 #26204055

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24×C8

Aliases

direct productD47×#1721

Splittings

FittingC47×#1721 ⋊ C2
SylowC47 ⋊ C2×#1721

Subgroups

subgroupG/H
centerC22#127×D47
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC47×#1721C2
socleC22×C47C2×#127
hypercenter#1721D47
hypocenterC47C2×#1721
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #1721

1146 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, 157345);