Finite Group Databasebeta

D47×#1281 #26105904

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productD47×#1281

Splittings

FittingC47×#1281 ⋊ C2
SylowC47 ⋊ C2×#1281

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC22×C47C2×C4×C8
FrattiniC2×C42C22×D47
FittingC47×#1281C2
socleC22×C47C2×#95
prime radicalC23×D47C42
cosocleC2×C42×C47C23
hypercenter#1281D47
hypocenterC47C2×#1281
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1281

678 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, 59194);