Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C32 |
| direct product | D4×C3⋊((C3⋊D3)⋊C3) |
| Fitting | C3×D4×H(3,𝔽3) ⋊ C2 |
| Sylow | C3×H(3,𝔽3) ⋊ C2×D4 |
822 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D4×((C3⋊D3)⋊C3)⋊D3, #72259996, #67×C3⋊((C3⋊D3)⋊C3) |
| maximal normal subgroup of | D4×((C3⋊D3)⋊C3)⋊D3 |
| maximal quotient of | D4×#92300, #72259996, #67×C3⋊((C3⋊D3)⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2631);