Finite Group Databasebeta

D47×#2337 #26375190

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productD47×#2337

Splittings

FittingC47×#2337 ⋊ C2
SylowC47 ⋊ C2×#2337

Subgroups

subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2337C2
socle, cosocleC23×C47C25
prime radicalC22×D4×D47C22
hypercenter#2337D47
hypocenterC47C2×#2337
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2337

3046 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328480);