Finite Group Databasebeta

C22×#15689017 #26374608

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

Aliases

direct productC22×#15689017

Splittings

SylowC47 ⋊ C22×#388

Subgroups

subgroupG/H
centerC25C22×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC23×C22⋊C4×C47C2
socleC25×C47C23
prime radicalC26×C47C22
cosocleC23×C47C25
hypercenterC23×C22⋊C4D47
hypocenterC47C22×#388
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C25 ◁ C23×C22⋊C4

5966 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 327898);