Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of 3−1+2⋊Q8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#3697⋊C3 |
| unambiguous semidirect product | #3697⋊C32 |
| unambiguous semidirect product | (C3×#3697)⋊C3 |
| Fitting | C2×C3×C4×3−1+2 ⋊ C2 |
| Sylow | C3×3−1+2 ⋊ #41 |
440 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 150 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 | #72219876, C3×#63495⋊C3, #72219923, … |
| maximal normal subgroup of | #72219876, C3×#63495⋊C3, #72219923, … |
| maximal quotient of | #72219876 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2559);