Finite Group Databasebeta

D47×#2243 #26371582

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C23×C4

Aliases

direct productD47×#2243

Splittings

FittingC47×#2243 ⋊ C2
SylowC47 ⋊ C2×#2243

Subgroups

subgroupG/H
centerC22C2×D8×D47
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#2243C2
socleC22×C47C22×D8
prime radicalC2×D8×D47C22
hypercenter#2243D47
hypocenterC47C2×#2243
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2243

634 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, 324872);