Finite Group Databasebeta

C2×#20242360 #26188460

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

Aliases

direct productC2×#20242360

Splittings

SylowC47 ⋊ C2×#1605

Subgroups

subgroupG/H
centerC23#13093992
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#451C2
socleC23×C47#120
prime radicalC24×C47C2×D4
hypercenterC2×#451D47
hypocenterC47C2×#1605
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

1200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

920 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 141750);