Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C3⋊((C3⋊D3)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C33 |
| direct product | C9×C3⋊((C3⋊D3)⋊C3) |
| unambiguous semidirect product | C3⋊(C9×(C3⋊D3)⋊C3) |
| Fitting, Sylow | C3×C9×H(3,𝔽3) ⋊ C2 |
| derived | C33 ⋊ C2×C3×C9 |
599 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 599 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #72243409, 3−1+2×C3⋊((C3⋊D3)⋊C3), C9×#92303, … |
| maximal normal subgroup of | 3−1+2×C3⋊((C3⋊D3)⋊C3), D3×C9×(C3⋊D3)⋊C3, #72253782, … |
| maximal quotient of | #72243409, C9×#92303, #72243885 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1430);