Finite Group Databasebeta

D47×#2164 #26369349

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productD47×#2164

Splittings

FittingC47×#2164 ⋊ C2
SylowC47 ⋊ C2×#2164

Subgroups

subgroupG/H
center, FrattiniC2×C8C23×D47
commutator, socleC22×C47C23×C8
FittingC47×#2164C2
prime radicalC23×D47C2×C8
cosocleC2×C8×C47C24
hypercenter#2164D47
hypocenterC47C2×#2164
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ #2164

610 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322639);