Finite Group Databasebeta

C2×#20242452 #26192132

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

Aliases

direct productC2×#20242452

Splittings

FittingC2×C47×#459 ⋊ C2
SylowC47 ⋊ C2×#1621

Subgroups

subgroupG/H
centerC23#13093992
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC2×C47×#459C2
socleC23×C47#120
hypercenterC2×#459D47
hypocenterC47C2×#1621
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

1438 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

926 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 145422);