Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (#11759813⋊C3)⋊D5 |
| unambiguous semidirect product | (#11759813⋊D5)⋊C3 |
| Fitting, socle, Hall | C5×C132 ⋊ C2×C3×D3 |
| derived | C5×#92789 ⋊ C22×C3 |
| Hall | C5×C13⋊C32 ⋊ C22 |
| Hall | C13⋊C32 ⋊ C2×D5 |
| Sylow | C132 ⋊ C3×D3×D5 |
| Sylow | C5 ⋊ (#11759813⋊C2)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×#92789 | C22×C3 |
| Fitting, socle | C5×C132 | C2×C3×D3 |
| LCS | G ▷ C5×#92789 | |
| UCS | C1 | |
160 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 160 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) = 130 |
Polycyclic presentation:
2^2,3^2,5,13^2|d^a=d^2,e^a=e^4,f^a=g,g^a=f,d^b=d^2,f^b=g^12,g^b=f^12,f^c=f^9,g^c=g^9,f^d=f^3,g^d=g^9104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 478);