Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3×C13 |
| direct product | C3×C5×#14523129 |
| derived, Sylow | C132 ⋊ C32×C4×C5 |
| Hall | C3×C5×#92789 ⋊ C4 |
| Hall | C5×#10621725 ⋊ C32 |
| Hall | C3×#92789 ⋊ C4×C5 |
| Hall | C5×C132 ⋊ C32×C4 |
| Hall | #10621725 ⋊ C32×C5 |
192 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2340 |
1020 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 397);