Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #634⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C32 |
| direct product | C2×C3×#634⋊C3 |
| unambiguous semidirect product | (C2×#634)⋊C32 |
| unambiguous semidirect product | (C2×C3×#634)⋊C3 |
| Sylow | C3×H(3,𝔽3) ⋊ C2×Q8 |
524 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
186 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2547);