Finite Group Databasebeta

C2×#20241599 #26137315

order12032
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20241599

Splittings

SylowC47 ⋊ C2×M128

Subgroups

subgroupG/H
centerC2×C32C2×D47
commutatorC2×C47C22×C32
FrattiniC32C22×D47
FittingC22×C32×C47C2
socleC22×C47C2×C32
prime radicalC23×C47C32
cosocleC32×C47C23
hypercenterC22×C32D47
hypocenterC47C2×M128
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C32 ◁ C22×C32

134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 90605);