Finite Group Databasebeta

D47×#1759 #26213992

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productD47×#1759

Splittings

FittingC47×#1759 ⋊ C2
SylowC47 ⋊ C2×#1759

Subgroups

subgroupG/H
centerC2×C4C2×D4×D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC47×#1759C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#41×D47C22
cosocleC22×C4×C47C24
hypercenter#1759D47
hypocenterC47C2×#1759
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

1662 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167282);