Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×D845 |
| Fitting, derived, Hall | C32×C5×C169 ⋊ C22 |
| Hall | C32×C169 ⋊ C2×D5 |
| Hall | C5×C169 ⋊ C2×C3⋊D3 |
| Sylow | C169 ⋊ D5×C3⋊D3 |
| Hall | C32×C5 ⋊ C2×D169 |
| Sylow | C32 ⋊ C2×D845 |
| Sylow | C5 ⋊ C3⋊D3×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C5×C169 | C22 |
| Frattini | C13 | C3⋊D3×D65 |
| socle | C32×C5×C13 | C2×D13 |
| LCS | G ▷ C32×C5×C169 | |
| UCS | C1 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
2544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 130);