Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×#11721790 |
| Fitting | C2×C3×C9×D8 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×AGL(1,ℤ/8) |
1490 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,ℤ/8)×C3⋊D9, C2×#72244273 |
| maximal normal subgroup of | C2×AGL(1,ℤ/8)×C3⋊D9 |
| maximal quotient of | C2×#72244273 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 20405);