Finite Group DatabasebetaFinite Group Databasebeta| order | 7290 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C35 |
| direct product | D5×#10624749 |
| Fitting, Hall | C5×#10624749 ⋊ C2 |
| Sylow | C5 ⋊ C2×#10624749 |
976 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 976 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 135 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#10624749, D5×#13091120, #72247336, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#10624749, D5×#13091120, #72247336, … |
Past the SmallGroups library coverage — no SmallGroups id.