Finite Group Databasebeta

D47×#1461 #26182082

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productD47×#1461

Splittings

FittingC47×#1461 ⋊ C2
SylowC47 ⋊ C2×#1461

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC22×C47C23×C8
FrattiniC22×C4C23×D47
FittingC47×#1461C2
socleC22×C47C22×C22⋊C4
prime radicalC23×D47C22×C4
cosocleC22×C4×C47C24
hypercenter#1461D47
hypocenterC47C2×#1461
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1461

1282 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, 135372);