Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C5×A4×#92788 |
| Fitting, socle, Hall | C22×C5×C132 ⋊ C32 |
| derived, Hall | C22×C132 ⋊ C32×C5 |
| Hall | C5×C132 ⋊ C3×A4 |
| Sylow | C132 ⋊ C3×C5×A4 |
| Hall | C22×C5 ⋊ C3×#92788 |
| Sylow | C22 ⋊ C3×C5×#92788 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | A4×#92788 |
| commutator, cosocle, hypocenter | C22×C132 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C132 | C32 |
| LCS | G ▷ C22×C132 | |
| UCS | C1 ◁ C5 | |
448 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3380 |
1180 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 732);