Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | C3×#92259 |
| Fitting, Sylow | C3×#6891 ⋊ C2 |
872 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | #72243421, C32×#92259, C3×3−1+2×(C3⋊D3)⋊C3, … |
| maximal normal subgroup of | C32×#92259, C3×3−1+2×(C3⋊D3)⋊C3, #72243496, … |
| maximal quotient of | #72243419, C32×#92259, #72243499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1475);