Finite Group Databasebeta

D47×#2132 #26369104

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD47×#2132

Splittings

FittingC47×#2132 ⋊ C2
SylowC47 ⋊ C2×#2132

Subgroups

subgroupG/H
centerC4#99×D47
commutatorC2×C4×C47C23×C4
FrattiniC2×Q8C23×D47
FittingC47×#2132C2
socleC2×C47C22×#99
prime radical#532×D47C2
cosocleC2×Q8×C47C24
hypercenter#2132D47
hypocenterC47C2×#2132
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #2132

1306 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, 322394);