Finite Group Databasebeta

C2×C3×#5477 #11900755

order1152
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C29

Aliases

direct productC2×C3×#5477

Splittings

FittingC22×C32×C42 ⋊ C2
SylowC32 ⋊ C2×#532

Subgroups

subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC22×C32×C42C2
socleC23×C32C24
hypercenterC22×C3×C42D3
hypocenterC3C2×C3×#532
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C22×C3×C42

3705 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 134766);