Finite Group Databasebeta

D47×#1284 #26105988

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productD47×#1284

Splittings

FittingC47×#1284 ⋊ C2
SylowC47 ⋊ C2×#1284

Subgroups

subgroupG/H
centerC22#95×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#1284C2
socleC22×C47C2×#95
prime radicalC24×D47D4
cosocleC23×C4×C47C23
hypercenter#1284D47
hypocenterC47C2×#1284
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

1118 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, 59278);