Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#10596473 |
| Fitting | C24×C32 ⋊ C2×D3 |
1114 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13181790, C3×#13164262, #72222948, … |
| maximal normal subgroup of | #72222977, C3×D3×D4×S4, D3×#10596473 |
| maximal quotient of | C3×#72215293 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 46795);