Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C33 |
| direct product | C3×C3⋊#4208 |
| unambiguous semidirect product | C3⋊(C3×#4208) |
| Fitting, Sylow | C32×#737 ⋊ C2 |
1811 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 1811 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | #72221827, #72221835, #72221866, … |
| maximal normal subgroup of | #72221835, #72221866, C2×C3×C3⋊#4208 |
| maximal quotient of | #72221823, #72221830, C2×C3×C3⋊#4208 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1776);