Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×#10592484 |
| Fitting | C33×#102 ⋊ C2 |
| Sylow | C33 ⋊ #442 |
992 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C3⋊D3×#442, #72254769, D3×#10592484, … |
| maximal normal subgroup of | C3×C3⋊D3×#442, D3×#10592484, #72268985 |
| maximal quotient of | #72254769 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 28885);