Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3×#63703 |
| derived | H(5,𝔽2) ⋊ C2×C3×C9 |
| Sylow | C2×H(5,𝔽2) ⋊ C3×C9 |
1106 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 1106 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72244951, C2×C3×#11722589, C2×#72244963, … |
| maximal normal subgroup of | C2×#72244951, C2×C3×#11722589, C2×#72244963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30948);