Finite Group DatabasebetaFinite Group Databasebeta| order | 3240 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D3×#10587380 |
| Fitting, derived, Hall | C3×C5×H(3,𝔽3) ⋊ C2×C4 |
| Sylow | C3×H(3,𝔽3) ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ D3×#1084 |
454 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 90 |
93 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽5)×#272, #72254535 |
| maximal normal subgroup of | D3×AGL(1,𝔽5)×#272 |
| maximal quotient of | #72254535 |
Past the SmallGroups library coverage — no SmallGroups id.