Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #3672⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#3672⋊C3 |
| unambiguous semidirect product | #3672⋊C32 |
| unambiguous semidirect product | (C3×#3672)⋊C3 |
| Sylow | C3×3−1+2 ⋊ SD16 |
260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
123 conjugacy classes — view the full character table.
| maximal subgroup of | #72219869, #72219901, C3×#63495⋊C3, … |
| maximal normal subgroup of | #72219869, #72219901, C3×#63495⋊C3, … |
| maximal quotient of | #72219869 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1581);