Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22 |
| direct product | 3−1+2×#237 |
| unambiguous semidirect product | (C9×#237)⋊C3 |
| Fitting | C3×D4×3−1+2 ⋊ C2 |
| Sylow | C3×3−1+2 ⋊ #41 |
408 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | #72219896, 3−1+2×#1004, #72219952, … |
| maximal normal subgroup of | 3−1+2×#1004, #72219952, #72219964 |
| maximal quotient of | #72219896 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2574);