Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D45×D169 |
| unambiguous semidirect product | (C5×D169)⋊D9 |
| unambiguous semidirect product | (C9×D169)⋊D5 |
| Fitting, derived, Hall | C5×C9×C169 ⋊ C22 |
| Hall | C9×C169 ⋊ C2×D5 |
| Hall | C5×C169 ⋊ C2×D9 |
| Sylow | C169 ⋊ C2×D45 |
| Hall | C5×C9 ⋊ C2×D169 |
| Sylow | C9 ⋊ D5×D169 |
| Sylow | C5 ⋊ D9×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C9×C169 | C22 |
| Frattini | C3×C13 | D13×D15 |
| socle | C3×C5×C13 | D3×D13 |
| LCS | G ▷ C5×C9×C169 | |
| UCS | C1 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
2064 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 38);