Finite Group Databasebeta

D47×#1867 #26217356

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

Aliases

direct productD47×#1867

Splittings

FittingC47×#1867 ⋊ C2
SylowC47 ⋊ C2×#1867

Subgroups

subgroupG/H
centerC22#120×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#1867C2
socleC22×C47C2×#120
prime radicalC22×D4×D47C22
cosocleC24×C47C24
hypercenter#1867D47
hypocenterC47C2×#1867
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ #1867

1994 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

800 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 170646);