Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #634⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C32 |
| direct product | C2×C3×C4⋊((C3⋊D3)⋊C3) |
| unambiguous semidirect product | (C2×C4⋊(C3⋊D3))⋊C32 |
| unambiguous semidirect product | (C2×C3×C4⋊(C3⋊D3))⋊C3 |
| Fitting | C2×C3×C4×H(3,𝔽3) ⋊ C2 |
| Sylow | C3×H(3,𝔽3) ⋊ C2×D4 |
684 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 684 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.
| maximal subgroup of | C2×C3×D4×(C3⋊D3)⋊C3, C2×C3×C4⋊#4183 |
| maximal normal subgroup of | C2×C3×D4×(C3⋊D3)⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2550);