Finite Group Databasebeta

D47×#2264 #26374414

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD47×#2264

Splittings

FittingC47×#2264 ⋊ C2
SylowC47 ⋊ C2×#2264

Subgroups

subgroupG/H
centerC2C2×D16×D47
commutator, cosocleC16×C47C24
FrattiniC16C23×D47
FittingC47×#2264C2
socleC2×C47C22×D16
prime radical#508×D47C2
hypercenter#2264D47
hypocenterC47C2×#2264
LCSG ▷ C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2264

462 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

650 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 327704);