Finite Group Databasebeta

D47×#2165 #26369396

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productD47×#2165

Splittings

FittingC47×#2165 ⋊ C2
SylowC47 ⋊ C2×#2165

Subgroups

subgroupG/H
centerC4#117×D47
commutatorC2×C4×C47C23×C4
FrattiniC2×C8C23×D47
FittingC47×#2165C2
socleC2×C47C2×#432
prime radicalC23×D47M16
cosocleC2×C8×C47C24
hypercenter#2165D47
hypocenterC47C2×#2165
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ #97 ◁ #2165

570 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, 322686);