Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | D4×#4177 |
| Fitting | D4×#731 ⋊ C2 |
| Sylow | #731 ⋊ C2×D4 |
286 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
65 conjugacy classes — view the full character table.
| maximal subgroup of | D4×#4176⋊C2, D4×#4177⋊C3 |
| maximal normal subgroup of | D4×#4176⋊C2, D4×#4177⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1073);