Finite Group Databasebeta

D47×#1388 #26131207

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productD47×#1388

Splittings

FittingC47×#1388 ⋊ C2
SylowC47 ⋊ C2×#1388

Subgroups

subgroupG/H
centerC4#102×D47
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC47×#1388C2
socleC2×C47C2×#340
prime radicalC23×D47Q16
cosocleC22×C8×C47C23
hypercenter#1388D47
hypocenterC47C2×#1388
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #1388

554 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, 84497);