Finite Group Databasebeta

D47×#2345 #26375517

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

Aliases

direct productD47×#2345

Splittings

FittingC47×#2345 ⋊ C2
SylowC47 ⋊ C2×#2345

Subgroups

subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2345C2
socle, cosocleC23×C47C25
prime radicalC24×D47C23
hypercenter#2345D47
hypocenterC47C2×#2345
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2345

3094 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328807);