Finite Group Databasebeta

D47×#1286 #26106052

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

Aliases

direct productD47×#1286

Splittings

FittingC47×#1286 ⋊ C2
SylowC47 ⋊ C2×#1286

Subgroups

subgroupG/H
centerC22#95×D47
commutatorC2×C4×C47C2×C42
FrattiniC2×C42C22×D47
FittingC47×#1286C2
socleC22×C47C2×#95
prime radicalC23×D47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1286D47
hypocenterC47C2×#1286
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

702 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, 59342);