Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C3×C5×#14523130 |
| derived, Sylow | C132 ⋊ C32×C4×C5 |
| Hall | C3×C5×#92788 ⋊ C4 |
| Hall | C5×C13×Dic13 ⋊ C32 |
| Hall | C3×#92788 ⋊ C4×C5 |
| Hall | C5×C132 ⋊ C32×C4 |
| Hall | C13×Dic13 ⋊ C32×C5 |
288 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 780 |
1200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 398);