Finite Group Databasebeta

C22×#15689037 #26382461

order12032
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productC22×#15689037

Splittings

SylowC47 ⋊ C22×#394

Subgroups

subgroupG/H
centerC25C22×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
Fitting, prime radicalC24×D4×C47C2
socleC25×C47C23
hypercenterC24×D4D47
hypocenterC47C22×#394
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C25 ◁ C24×D4

8798 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 335751);