Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of 3−1+2⋊Q8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3×#611⋊C3 |
| unambiguous semidirect product | (C2×#611)⋊C32 |
| unambiguous semidirect product | (C2×C3×#611)⋊C3 |
| Fitting | C23×C3×3−1+2 ⋊ C2 |
| Sylow | C3×3−1+2 ⋊ C2×D4 |
646 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 178 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, C2×#88668⋊C3, C3×#63710⋊C3, … |
| maximal normal subgroup of | C2×#14517439, C2×#88668⋊C3, C3×#63710⋊C3, … |
| maximal quotient of | C2×#14517439, C3×#63495⋊C3, C3×#63499⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2597);