Finite Group Databasebeta

D47×#1470 #26182229

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD47×#1470

Splittings

FittingC47×#1470 ⋊ C2
SylowC47 ⋊ C2×#1470

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1470C2
socleC22×C47C22×C22⋊C4
prime radicalC23×D47C22×C4
cosocleC22×C4×C47C24
hypercenter#1470D47
hypocenterC47C2×#1470
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1470

1002 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

800 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 135519);