Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×D9×D65 |
| unambiguous semidirect product | (C5×D9)⋊(C13×D13) |
| unambiguous semidirect product | (C13×D9)⋊(D5×C13) |
| Fitting, Hall | C5×C9×C132 ⋊ C22 |
| derived | C5×C9×C13 ⋊ C22×C13 |
| Hall | C9×C132 ⋊ C2×D5 |
| Hall | C5×C132 ⋊ C2×D9 |
| Sylow | C132 ⋊ D5×D9 |
| Hall | C5×C9 ⋊ C2×C13×D13 |
| Sylow | C9 ⋊ C2×C13×D65 |
| Sylow | C5 ⋊ C13×D9×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D9×D65 |
| commutator, cosocle, hypocenter | C5×C9×C13 | C22×C13 |
| Frattini | C3 | D3×C13×D65 |
| Fitting | C5×C9×C132 | C22 |
| socle | C3×C5×C132 | C2×D3 |
| LCS | G ▷ C5×C9×C13 | |
| UCS | C1 ◁ C13 | |
192 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1170 |
2652 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 360);