Finite Group Databasebeta

D47×#2003 #26243166

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productD47×#2003

Splittings

FittingC47×#2003 ⋊ C2
SylowC47 ⋊ C2×#2003

Subgroups

subgroupG/H
centerC22#120×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2003C2
socleC22×C47C2×#120
prime radicalC2×AGL(1,ℤ/8)×D47C2
hypercenter#2003D47
hypocenterC47C2×#2003
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2003

2126 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, 196456);