Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C13×D585 |
| unambiguous semidirect product | (C2×C5)⋊(C13×D117) |
| unambiguous semidirect product | (C2×C9)⋊(C13×D65) |
| unambiguous semidirect product | (C2×C13)⋊(C13×D45) |
| Fitting | C2×C5×C9×C132 ⋊ C2 |
| derived | C5×C9×C13 ⋊ C22×C13 |
| Hall | C5×C9×C132 ⋊ C22 |
| Hall | C9×C132 ⋊ C2×D5 |
| Hall | C5×C132 ⋊ C2×D9 |
| Sylow | C132 ⋊ C2×D45 |
| Hall | C5×C9 ⋊ C2×C13×D13 |
| Sylow | C9 ⋊ C2×C13×D65 |
| Sylow | C5 ⋊ C2×C13×D117 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D585 |
| commutator, cosocle, hypocenter | C5×C9×C13 | C22×C13 |
| Frattini | C3 | C2×C13×D195 |
| Fitting | C2×C5×C9×C132 | C2 |
| socle | C2×C3×C5×C132 | D3 |
| LCS | G ▷ C5×C9×C13 | |
| UCS | C1 ◁ C2×C13 | |
192 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2340 |
7644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 376);