Finite Group Databasebeta

C22×#15689014 #26374605

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

Aliases

direct productC22×#15689014

Splittings

FittingC23×C42×C47 ⋊ C2
SylowC47 ⋊ C22×#388

Subgroups

subgroupG/H
centerC25C22×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC23×C42×C47C2
socleC25×C47C23
prime radicalC25×D47C22
cosocleC23×C47C25
hypercenterC23×C42D47
hypocenterC47C22×#388
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C25 ◁ C23×C42

5966 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, 327895);