Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×#15690150 |
| derived, Sylow | C132 ⋊ C22×C5×C9 |
| Hall | C5×#13095200 ⋊ C22 |
| Hall | C2×C5×C13×D13 ⋊ C9 |
| Hall | #13095200 ⋊ C22×C5 |
| Hall | C5×C132 ⋊ C22×C9 |
| Hall | C2×C13×D13 ⋊ C5×C9 |
192 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2340 |
1200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 293);