Finite Group Databasebeta

D47×#1391 #26131231

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

Aliases

direct productD47×#1391

Splittings

FittingC47×#1391 ⋊ C2
SylowC47 ⋊ C2×#1391

Subgroups

subgroupG/H
centerC4#99×D47
commutatorC23×C47C2×C42
FrattiniC2×#41C22×D47
FittingC47×#1391C2
socleC2×C47C2×#342
prime radicalC2×#41×D47C22
cosocleC2×#41×C47C23
hypercenter#1391D47
hypocenterC47C2×#1391
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1391

782 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

650 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84521);