Finite Group Databasebeta

C2×#20242352 #26188376

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

Aliases

direct productC2×#20242352

Splittings

SylowC47 ⋊ C2×#1603

Subgroups

subgroupG/H
centerC23#13093994
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#327C2
socleC23×C47#120
prime radicalC2×#121×C47C22
hypercenterC2×#327D47
hypocenterC47C2×#1603
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

1232 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, 141666);