Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C22×C32 |
| direct product | C22×#66440 |
| Fitting | C24×3−1+2 ⋊ C3 |
| Sylow | C24 ⋊ #737 |
482 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#11758104, #72259666, #72259686 |
| maximal normal subgroup of | C22×#11758104, #72259666, #72259686 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3048);