Finite Group DatabasebetaFinite Group Databasebeta| order | 2430 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | D5×#6909 |
| Fitting, Hall | C5×#6909 ⋊ C2 |
| Sylow | C5 ⋊ C2×#6909 |
296 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 135 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#6909, D5×#10624749, D5×#4183⋊C3, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#6909, D5×#10624749, D5×#4183⋊C3, … |
Past the SmallGroups library coverage — no SmallGroups id.