Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×#89039 |
| Fitting | C22×C34 ⋊ C22 |
| Sylow | C34 ⋊ C2×D4 |
1220 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 1220 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
153 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#89039, C3×#11724611, #72220357, … |
| maximal normal subgroup of | D3×#89039, C3×#11724611, #72220357, … |
| maximal quotient of | #72228838, #72259553, #72259655, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3366);