Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #23778489⋊C3 |
| unambiguous semidirect product | #23778490⋊C3 |
| unambiguous semidirect product | #23778495⋊C3 |
| Fitting, socle, derived, Hall | C5×C132 ⋊ C32×C4 |
| Hall | C5×C13⋊C32 ⋊ C4 |
| Hall | #16810010 ⋊ C32 |
| Hall | C13⋊C32 ⋊ Dic5 |
| Sylow | C132 ⋊ C32×Dic5 |
| Sylow | C5 ⋊ #14523144⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C132 | C32×C4 |
| prime radical | C5×(C13⋊C3)⋊(D13⋊C3) | C2 |
| cosocle | C5×C13⋊D13 | C2×C32 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 | |
192 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 195 |
Polycyclic presentation:
2,3^2,2,5,13^2|a^2=d,e^a=e^4,f^a=f^5,g^a=g^5,f^b=f^3,f^c=f^3,g^c=g^3,f^d=f^12,g^d=g^12122 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 484);