Finite Group Databasebeta

C2×C32×#5077 #72269492

order3456
automorphism?
homologyAbelianization (H1) = C24×C32 · Schur multiplier (H2) = C26×C3

Aliases

direct productC2×C32×#5077

Splittings

FittingC2×C33×#127 ⋊ C2
SylowC33 ⋊ C2×#453

Subgroups

subgroupG/H
centerC22×C32#937
commutator, cosocleC2×C3×C4C24×C32
FrattiniC2×C4C23×C32×D3
FittingC2×C33×#127C2
socleC22×C33#120
hypercenterC2×C32×#127D3
hypocenterC3C2×C32×#453
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C22×C32×C4 ◁ C2×C32×#127

7056 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.