Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D3×C5⋊(D169⋊C3) |
| unambiguous semidirect product | (C5×D3)⋊(D169⋊C3) |
| unambiguous semidirect product | (D3×C169⋊C3)⋊D5 |
| unambiguous semidirect product | (D3×D845)⋊C3 |
| Fitting, derived | C3×C5×C169 ⋊ C22×C3 |
| Hall | C3×C5×C169⋊C3 ⋊ C22 |
| Hall | C3×C169⋊C3 ⋊ C2×D5 |
| Hall | C5×C169 ⋊ C2×C3×D3 |
| Sylow | C169 ⋊ C3×D3×D5 |
| Sylow | C5 ⋊ D3×D169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C5×C169 | C22×C3 |
| Frattini | C13 | D3×C5⋊(D13⋊C3) |
| socle | C3×C5×C13 | C2×D13⋊C3 |
| LCS | G ▷ C3×C5×C169 | |
| UCS | C1 | |
132 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2535 |
456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 90);