Finite Group Databasebeta

D47×#1841 #26216539

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

Aliases

direct productD47×#1841

Splittings

FittingC47×#1841 ⋊ C2
SylowC47 ⋊ C2×#1841

Subgroups

subgroupG/H
centerC4#117×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1841C2
socleC2×C47C2×#383
prime radicalC23×D47#41
cosocleC22×C4×C47C24
hypercenter#1841D47
hypocenterC47C2×#1841
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×M16 ◁ #1841

730 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

800 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 169829);