Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #88941 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#88942 |
| Sylow | C34 ⋊ SD16 |
254 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
81 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13049364, #72220225, C3×#11724350, … |
| maximal normal subgroup of | #72220225, C3×#11724350, #72220276 |
| maximal quotient of | C3×#11722796, C3×#72277538 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3147);