Finite Group Databasebeta

D47×#2041 #26243942

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

Aliases

direct productD47×#2041

Splittings

FittingC47×#2041 ⋊ C2
SylowC47 ⋊ C2×#2041

Subgroups

subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2041C2
socleC23×C47C22×D4
prime radicalC2×#127×D47C2
hypercenter#2041D47
hypocenterC47C2×#2041
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2041

2230 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, 197232);