Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of A4×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C22 |
| direct product | C2×D9×C22⋊C9 |
| derived | C22×C9 ⋊ C22×C9 |
240 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C22⋊C9×(C22⋊C9)⋊C2, C2×#14518201 |
| maximal normal subgroup of | C2×#14518201 |
| maximal quotient of | C2×C22⋊C9×(C22⋊C9)⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1846);