Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #41×((C3⋊D3)⋊C3)⋊C2 |
| Fitting | #41×H(3,𝔽3) ⋊ C22 |
| Sylow | H(3,𝔽3) ⋊ C22×#41 |
3279 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | #41×AGL(2,𝔽3), AGL(1,ℤ/8)×((C3⋊D3)⋊C3)⋊C2, H(5,𝔽2)×((C3⋊D3)⋊C3)⋊C2 |
| maximal normal subgroup of | AGL(1,ℤ/8)×((C3⋊D3)⋊C3)⋊C2, H(5,𝔽2)×((C3⋊D3)⋊C3)⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30851);