Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #23778414⋊C3 |
| derived | C5×#92789 ⋊ C3×C4 |
| Hall | C5×C13⋊C32 ⋊ C4 |
| Hall | C13⋊C32 ⋊ Dic5 |
| Hall | C5×C132 ⋊ C3×Dic3 |
| Sylow | C132 ⋊ C3×Dic15 |
| Sylow | C5 ⋊ #14523126⋊C3 |
112 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 260 |
Polycyclic presentation:
2,3^2,5,13^2,2|a^2=g,c^a=c^2,d^a=d^4,e^a=f,f^a=e,e^b=e^9,f^b=f^9,e^c=e^3,f^c=f^9266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 393);