Finite Group Databasebeta

D47×#2225 #26370897

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

Aliases

direct productD47×#2225

Splittings

FittingC47×#2225 ⋊ C2
SylowC47 ⋊ C2×#2225

Subgroups

subgroupG/H
centerC22C2×D8×D47
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#2225C2
socleC22×C47C22×D8
prime radicalC22×D47C2×D8
hypercenter#2225D47
hypocenterC47C2×#2225
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2225

574 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, 324187);