Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C9×#997 |
| Fitting | C2×C9×H(5,𝔽2) ⋊ C3 |
| derived | H(5,𝔽2) ⋊ C2×C3×C9 |
| Sylow | C2×H(5,𝔽2) ⋊ C3×C9 |
683 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 683 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C2×3−1+2×#997, C2×D9×#997, C2×C9×#5935 |
| maximal normal subgroup of | C2×3−1+2×#997, C2×D9×#997, C2×C9×#5935 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30935);