Finite Group Databasebeta

C2×#20245467 #26370662

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

Aliases

direct productC2×#20245467

Splittings

SylowC47 ⋊ C2×#2214

Subgroups

subgroupG/H
centerC22#15689316
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC2×C47×#510C2
socleC22×C47#459
prime radicalC2×#135×C47C22
hypercenterC2×#510D47
hypocenterC47C2×#2214
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

686 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 323952);