Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D65⋊D117 |
| Fitting, derived, Hall | C5×C9×C132 ⋊ C22 |
| Hall | C9×C132 ⋊ C2×D5 |
| Hall | C5×C132 ⋊ C2×D9 |
| Sylow | C132 ⋊ D5×D9 |
| Hall | C5×C9 ⋊ D132 |
| Sylow | C9 ⋊ D65⋊D13 |
| Sylow | C5 ⋊ D13×D117 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C9×C132 | C22 |
| Frattini | C3 | D65⋊D39 |
| socle | C3×C5×C132 | C2×D3 |
| LCS | G ▷ C5×C9×C132 | |
| UCS | C1 | |
192 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 35 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^2,d^a=d^4,e^a=e^12,c^b=c^2g,e^b=e^12,f^b=f^12,g^b=g^22004 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 366);