Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | D3×C9⋊H(3,𝔽3) |
| unambiguous semidirect product | C3⋊(C2×C9⋊H(3,𝔽3)) |
| unambiguous semidirect product | (D3×C9)⋊H(3,𝔽3) |
| Fitting, Sylow | C3×C9⋊H(3,𝔽3) ⋊ C2 |
581 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 581 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
153 conjugacy classes — view the full character table.
| maximal subgroup of | #72243509, #72243510, D3×H(3,𝔽3)×3−1+2, … |
| maximal normal subgroup of | D3×H(3,𝔽3)×3−1+2, D3×D9⋊H(3,𝔽3), D3×#92262, … |
| maximal quotient of | #72243509, #72243510, #72243823, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1480);