Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#89028 |
| Sylow | C34 ⋊ #41 |
924 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | #72220317, C3×#11724408, #72220338, … |
| maximal normal subgroup of | #72220317, C3×#11724408, #72220338, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3358);