Finite Group Databasebeta

C2×#20244512 #26243508

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C28

Aliases

direct productC2×#20244512

Splittings

FittingC2×C47×#534 ⋊ C2
SylowC47 ⋊ C2×#2021

Subgroups

subgroupG/H
centerC23#13093993
commutator, cosocleC24×C47C24
FrattiniC24C23×D47
FittingC2×C47×#534C2
socleC23×C47#120
hypercenterC2×#534D47
hypocenterC47C2×#2021
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ C2×#534

3986 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 196798);