Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊(D13⋊C9))⋊D13 |
| unambiguous semidirect product | ((C13⋊C9)⋊D13)⋊D5 |
| derived, Hall | C5×C132 ⋊ C22×C9 |
| Hall | C5×C13×C13⋊C9 ⋊ C22 |
| Hall | D65⋊D13 ⋊ C9 |
| Hall | C13×C13⋊C9 ⋊ C2×D5 |
| Sylow | C132 ⋊ C2×C9×D5 |
| Sylow | C5 ⋊ D13×D13⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C5⋊(D13⋊C3))⋊D13 |
| commutator, hypocenter | C5×C132 | C22×C9 |
| Fitting, socle, cosocle | C3×C5×C132 | C22×C3 |
| prime radical | C3×D65⋊D13 | C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C3 | |
136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 136 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) = 1170 |
Polycyclic presentation:
2^2,3,5,13^2,3|c^3=g,d^a=d^4,e^a=e^12,e^b=e^12,f^b=f^12,e^c=e^3492 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 282);