Finite Group Databasebeta

D47×#1585 #26185813

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

Aliases

direct productD47×#1585

Splittings

FittingC47×#1585 ⋊ C2
SylowC47 ⋊ C2×#1585

Subgroups

subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1585C2
socleC22×C47C2×C4×D4
prime radicalC2×D4×D47C2×C4
cosocleC42×C47C24
hypercenter#1585D47
hypocenterC47C2×#1585
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1585

762 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 139103);