Finite Group Databasebeta

C2×#20245771 #26374549

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×#20245771

Splittings

SylowC47 ⋊ C2×#2280

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC25×C4×C47C2
socleC24×C47C24
prime radicalC26×C47C22
cosocleC23×C47C25
hypercenterC25×C4D47
hypocenterC47C2×#2280
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C25×C4

7630 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 327839);