Finite Group DatabasebetaFinite Group Databasebeta| order | 6600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | D3×(C11⋊C5)⋊AGL(1,𝔽5) |
| Fitting, socle, derived | C3×C5×C11 ⋊ C2×C4×C5 |
| Hall | C3×C5×C11⋊C5 ⋊ C2×C4 |
| Hall | C5×C11⋊C5 ⋊ C4×D3 |
| Hall | C3×C11 ⋊ C2×C5×AGL(1,𝔽5) |
| Sylow | C11 ⋊ C5×D3×AGL(1,𝔽5) |
| Sylow | C3 ⋊ C2×(C11⋊C5)⋊AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C11 | C2×C4×C5 |
| prime radical | D3×D5×C11⋊C5 | C2 |
| cosocle | C3×D5×C11 | C22×C5 |
| LCS | G ▷ C3×C5×C11 | |
| UCS | C1 | |
136 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 165 |
87 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.