Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #1088⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×(((C3⋊D3)⋊C3)⋊C2)⋊C4 |
| unambiguous semidirect product | (((C3⋊D3)⋊C3)⋊C2)⋊(C3×C4) |
| Sylow | C3×H(3,𝔽3) ⋊ C22⋊C4 |
240 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | #72259739, #72260000 |
| maximal normal subgroup of | #72260000 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1963);