Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | C2×#611⋊C9 |
| unambiguous semidirect product | (C2×#611)⋊C9 |
| Fitting | C23×C9⋊C9 ⋊ C2 |
| Sylow | C9⋊C9 ⋊ C2×D4 |
307 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 307 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
186 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14517439, #72219942, #72220016, … |
| maximal normal subgroup of | C2×#14517439, #72219942, #72220016, … |
| maximal quotient of | #72219908, #72220016, #72220060, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1112);