Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3×C4 |
| direct product | C2×C3×#64149 |
| Fitting | C22×C33×D4 ⋊ C2 |
| Sylow | C33 ⋊ C2×#127 |
3932 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C3⋊D3×#127, AGL(1,𝔽7)×#64149, C2×C3×#10592940, … |
| maximal normal subgroup of | C2×C3×C3⋊D3×#127, C2×C3×#10592940, C2×C3×#10591522, … |
| maximal quotient of | AGL(1,𝔽7)×#64149 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45608);