Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C9 · Schur multiplier (H2) = C34 |
| direct product | D3×C9×H(3,𝔽3) |
| unambiguous semidirect product | C3⋊(C2×C9×H(3,𝔽3)) |
| Fitting, Sylow | C3×C9×H(3,𝔽3) ⋊ C2 |
725 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 725 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
297 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72243489, D3×H(3,𝔽3)×3−1+2, C9×D9⋊H(3,𝔽3), … |
| maximal normal subgroup of | D3×H(3,𝔽3)×3−1+2, D3×D9×H(3,𝔽3), D3×C9×(C3⋊D3)⋊C3, … |
| maximal quotient of | #72243489, C9×D9⋊H(3,𝔽3), #72243817 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1429);