Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C32 |
| direct product | 3−1+2×#41⋊C3 |
| Fitting | #41×3−1+2 ⋊ C3 |
| Sylow | #41 ⋊ C3×3−1+2 |
230 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | #72245011, 3−1+2×2−1+4⋊C3, #72245682, … |
| maximal normal subgroup of | 3−1+2×2−1+4⋊C3, #72245682, #72245716 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2528);