Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of ((C22⋊C9)⋊C2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#1094⋊C4 |
| unambiguous semidirect product | ((C22⋊C9)⋊C4)⋊C32 |
| unambiguous semidirect product | (C3×(C22⋊C9)⋊C4)⋊C3 |
| derived | C22⋊C9 ⋊ C32×C4 |
264 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
114 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#1094⋊C4, #72245167, A4×#1094⋊C4, … |
| maximal normal subgroup of | C2×C3×#1094⋊C4, #72245167, C3×#63694⋊C3 |
| maximal quotient of | C2×C3×#1094⋊C4, #72245167, A4×#1094⋊C4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2094);