Finite Group Databasebeta

D47×#1381 #26131163

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productD47×#1381

Splittings

FittingC47×#1381 ⋊ C2
SylowC47 ⋊ C2×#1381

Subgroups

subgroupG/H
centerC2×C4D8×D47
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC47×#1381C2
socleC22×C47C2×#107
prime radicalC23×D47Q16
cosocleC22×C8×C47C23
hypercenter#1381D47
hypocenterC47C2×#1381
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1381

574 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, 84453);