Finite Group Databasebeta

D47×#1904 #26218156

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD47×#1904

Splittings

FittingC47×#1904 ⋊ C2
SylowC47 ⋊ C2×#1904

Subgroups

subgroupG/H
centerC2#386×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1904C2
socleC2×C47C2×#386
prime radicalC2×AGL(1,ℤ/8)×D47C2
cosocleC22×C4×C47C24
hypercenter#1904D47
hypocenterC47C2×#1904
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1904

1894 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

725 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 171446);