Finite Group Databasebeta

C2×#20244598 #26243863

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20244598

Splittings

FittingC2×C47×#390 ⋊ C2
SylowC47 ⋊ C2×#2037

Subgroups

subgroupG/H
centerC23#13093992
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#390C2
socleC23×C47#120
prime radicalC2×#15689690C2
hypercenterC2×#390D47
hypocenterC47C2×#2037
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#390

1714 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 197153);