Finite Group Databasebeta

D47×#2185 #26370023

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD47×#2185

Splittings

FittingC47×#2185 ⋊ C2
SylowC47 ⋊ C2×#2185

Subgroups

subgroupG/H
centerC22C2×D8×D47
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#2185C2
socleC22×C47C22×D8
prime radical#466×D47C2
hypercenter#2185D47
hypocenterC47C2×#2185
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2185

1178 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, 323313);