Finite Group DatabasebetaFinite Group Databasebeta| order | 6600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×AGL(1,𝔽5)×AGL(1,𝔽11) |
| Fitting, socle | C3×C5×C11 ⋊ C2×C4×C5 |
| derived | C5×C11 ⋊ C2×C3×C4×C5 |
| Hall | C3×C5×C11⋊C5 ⋊ C2×C4 |
| Hall | C5×C11⋊C5 ⋊ C2×C3×C4 |
| Hall | C3×C11 ⋊ C2×C5×AGL(1,𝔽5) |
| Sylow | C11 ⋊ C2×C3×C5×AGL(1,𝔽5) |
136 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 165 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽5)×AGL(1,𝔽11) |
| maximal normal subgroup of | D3×AGL(1,𝔽5)×AGL(1,𝔽11) |
Past the SmallGroups library coverage — no SmallGroups id.