Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C13 |
| direct product | AGL(1,𝔽5)×#13095201 |
| derived, Hall | C5×C132 ⋊ C4×C9 |
| Hall | C5×#13095201 ⋊ C4 |
| Hall | C132×AGL(1,𝔽5) ⋊ C9 |
| Sylow | C132 ⋊ C9×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×#13095201 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | AGL(1,𝔽5)×#92789 |
| commutator, hypocenter | C5×C132 | C4×C9 |
| Fitting, socle | C3×C5×C132 | C3×C4 |
| prime radical, cosocle | C3×D5×C132 | C2×C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C3 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 585 |
885 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 254);