Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#6194⋊C3 |
| unambiguous semidirect product | (C2×#6194)⋊C3 |
| Sylow | C3×3−1+2 ⋊ C2×D4 |
446 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#611⋊C3, C2×#67×AGL(1,ℤ/9), C2×#88646⋊C3 |
| maximal normal subgroup of | C2×D3×#611⋊C3, C2×#67×AGL(1,ℤ/9), C2×#88646⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2342);