Finite Group Databasebeta

D47×#2231 #26371010

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

Aliases

direct productD47×#2231

Splittings

FittingC47×#2231 ⋊ C2
SylowC47 ⋊ C2×#2231

Subgroups

subgroupG/H
centerC2#476×D47
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#2231C2
socleC2×C47C2×#476
prime radical#135×D47C22
hypercenter#2231D47
hypocenterC47C2×#2231
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2231

526 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

575 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 324300);