Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊((C13⋊C3)⋊D13) |
| Fitting, socle, derived | C3×C5×C132 ⋊ C22×C3 |
| Hall | C3×C5×C13×C13⋊C3 ⋊ C22 |
| Hall | C3×C13×C13⋊C3 ⋊ C2×D5 |
| Hall | C5×C132 ⋊ C2×C3×D3 |
| Sylow | C132 ⋊ C3×D3×D5 |
| Sylow | C5 ⋊ D3×(C13⋊C3)⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C132 | C22×C3 |
| LCS | G ▷ C3×C5×C132 | |
| UCS | C1 | |
256 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 256 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) = 585 |
Polycyclic presentation:
2^2,3^2,5,13^2|e^a=e^4,f^a=f^12,g^a=g^12,d^b=d^2,e^b=e^4,f^c=f^3432 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 698);