Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #6226 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3×#6233 |
| Fitting | C23×C32×C9 ⋊ C2 |
| Sylow | C32×C9 ⋊ C2×D4 |
780 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
342 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×D4×C3⋊D9, C2×#14517648 |
| maximal normal subgroup of | C2×C3×D4×C3⋊D9 |
| maximal quotient of | C2×#14517648 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2657);