Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C3⋊#14523151 |
| unambiguous semidirect product | C3⋊(C5×#14523151) |
| Fitting, socle | C3×C5×C132 ⋊ C3×C4 |
| derived | C3×C132 ⋊ C3×C4×C5 |
| Hall | C3×C5×C13×C13⋊C3 ⋊ C4 |
| Hall | C3×C13×C13⋊C3 ⋊ C4×C5 |
| Hall | C5×C132 ⋊ C3×Dic3 |
| Sylow | C132 ⋊ C3×C5×Dic3 |
128 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1170 |
420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 592);