Finite Group Databasebeta

D47×#1757 #26213974

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

Aliases

direct productD47×#1757

Splittings

FittingC47×#1757 ⋊ C2
SylowC47 ⋊ C2×#1757

Subgroups

subgroupG/H
centerC8C22⋊C4×D47
commutatorC22×C47C22×C42
FrattiniC22×C4C23×D47
FittingC47×#1757C2
socleC2×C47C2×C4×C22⋊C4
prime radicalC2×#41×D47C22
cosocleC22×C4×C47C24
hypercenter#1757D47
hypocenterC47C2×#1757
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C8 ◁ C22×C8 ◁ #1757

1474 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, 167264);