Finite Group Databasebeta

D47×#1378 #26131141

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productD47×#1378

Splittings

FittingC47×#1378 ⋊ C2
SylowC47 ⋊ C2×#1378

Subgroups

subgroupG/H
centerC8C22⋊C4×D47
commutatorC22×C47C2×C4×C8
FrattiniC22×C8C22×D47
FittingC47×#1378C2
socleC2×C47C2×#336
prime radicalC23×D47C2×C8
cosocleC22×C8×C47C23
hypercenter#1378D47
hypocenterC47C2×#1378
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C8 ◁ C22×C8 ◁ #1378

586 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, 84431);