Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C3 |
| direct product | C13×#14556844 |
| Fitting, socle, Hall | C32×C5×C132 ⋊ C4 |
| derived | C32×C5×C13 ⋊ C4×C13 |
| Hall | C32×C132 ⋊ AGL(1,𝔽5) |
| Hall | C5×C132 ⋊ #157 |
| Sylow | C132 ⋊ #4380 |
| Hall | C32×C5 ⋊ C13×Dic13 |
| Sylow | C32 ⋊ C13×#63120 |
| Sylow | C5 ⋊ C13×#90865 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #14556844 |
| commutator, hypocenter | C32×C5×C13 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C132 | C4 |
| prime radical | C132×C3⋊D15 | C2 |
| cosocle | C13×C3⋊D15 | C2×C13 |
| LCS | G ▷ C32×C5×C13 | |
| UCS | C1 ◁ C13 | |
224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 390 |
2067 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 784);