Finite Group Databasebeta

D47×#1784 #26215428

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productD47×#1784

Splittings

FittingC47×#1784 ⋊ C2
SylowC47 ⋊ C2×#1784

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1784C2
socleC22×C47C22×C22⋊C4
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenter#1784D47
hypocenterC47C2×#1784
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1784

3798 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

800 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168718);