Finite Group Databasebeta

D47×#2121 #26369001

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD47×#2121

Splittings

FittingC47×#2121 ⋊ C2
SylowC47 ⋊ C2×#2121

Subgroups

subgroupG/H
centerC2C2×#99×D47
commutatorC23×C47C23×C4
FrattiniC2×D4C23×D47
FittingC47×#2121C2
socleC2×C47C22×#99
prime radical#534×D47C2
cosocleC2×D4×C47C24
hypercenter#2121D47
hypocenterC47C2×#2121
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ #2121

1494 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

575 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322291);