Finite Group Databasebeta

C2×#20242679 #26197402

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20242679

Splittings

FittingC2×C47×#496 ⋊ C2
SylowC47 ⋊ C2×#1656

Subgroups

subgroupG/H
centerC23#13093992
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC2×C47×#496C2
socleC23×C47#120
hypercenterC2×#496D47
hypocenterC47C2×#1656
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

1138 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

776 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 150692);