Finite Group Databasebeta

D47×#1729 #26213634

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productD47×#1729

Splittings

FittingC47×#1729 ⋊ C2
SylowC47 ⋊ C2×#1729

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C22×C42
FittingC47×#1729C2
socleC23×C47C23×C4
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenter#1729D47
hypocenterC47C2×#1729
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1729

2350 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 166924);