Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×C3×A4×#67 |
| unambiguous semidirect product | (C23×#67)⋊C32 |
| unambiguous semidirect product | (C23×C3×#67)⋊C3 |
| Fitting | C25×C32 ⋊ C2×C3 |
1854 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C2×A4×((C22⋊C9)⋊C2)⋊C3, C3×A4×#953 |
| maximal normal subgroup of | C3×A4×#953 |
| maximal quotient of | C2×#67×#1094, C3×A4×#953 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47518);