Finite Group Databasebeta

D47×#1744 #26213737

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C42

Aliases

direct productD47×#1744

Splittings

FittingC47×#1744 ⋊ C2
SylowC47 ⋊ C2×#1744

Subgroups

subgroupG/H
centerC2×C42C22×D47
commutatorC2×C47C22×C4×C8
FrattiniC22×C4C23×D47
FittingC47×#1744C2
socleC23×C47C23×C4
prime radicalC23×D47C22×C4
cosocleC22×C4×C47C24
hypercenter#1744D47
hypocenterC47C2×#1744
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ #1744

1438 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167027);