Finite Group Databasebeta

C22×C3×#882 #11900249

order1152
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C211

Aliases

direct productC22×C3×#882

Splittings

FittingC22×C32×C22⋊C4 ⋊ C2
SylowC32 ⋊ C22×#120

Subgroups

subgroupG/H
centerC24×C3C22×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC22×C32×C22⋊C4C2
socleC24×C32C23
hypercenterC22×C3×C22⋊C4D3
hypocenterC3C22×C3×#120
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C22⋊C4

9425 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 134260);