Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#23778466 |
| Fitting, socle | C3×C5×C132 ⋊ C3×C4 |
| derived, Hall | C5×C132 ⋊ C32×C4 |
| Hall | C3×C5×C13×C13⋊C3 ⋊ C4 |
| Hall | #16810004 ⋊ C32 |
| Hall | C3×C13×C13⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C132 ⋊ C32×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3×#14523151 |
160 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1170 |
375 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 524);