Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C32×#833 |
| Sylow | C33 ⋊ C2×#100 |
2060 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×#10591503, C2×C32×#5077, C2×C3×#10591510 |
| maximal normal subgroup of | C2×C3×#10591503, C2×C32×#5077, C2×C3×#10591510 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 28717);