Finite Group Databasebeta

D47×#2180 #26369707

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD47×#2180

Splittings

FittingC47×#2180 ⋊ C2
SylowC47 ⋊ C2×#2180

Subgroups

subgroupG/H
centerC2#442×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC47×#2180C2
socleC2×C47C2×#442
prime radical#135×D47C22
cosocleC2×C8×C47C24
hypercenter#2180D47
hypocenterC47C2×#2180
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #2180

646 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, 322997);