Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D13×C13⋊C9 |
| derived, Sylow | C132 ⋊ C22×C5×C9 |
| Hall | C5×C13×C13⋊C9 ⋊ C22 |
| Hall | C2×C5×C13×D13 ⋊ C9 |
| Hall | C13×C13⋊C9 ⋊ C22×C5 |
| Hall | C5×C132 ⋊ C22×C9 |
| Hall | C2×C13×D13 ⋊ C5×C9 |
136 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2340 |
1680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 296);