Finite Group Databasebeta

D47×#1811 #26215893

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD47×#1811

Splittings

FittingC47×#1811 ⋊ C2
SylowC47 ⋊ C2×#1811

Subgroups

subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1811C2
socleC22×C47C22×C4⋊C4
prime radicalC24×D47Q8
cosocleC22×C4×C47C24
hypercenter#1811D47
hypocenterC47C2×#1811
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1811

1438 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, 169183);