Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | Dic5×#13095200 |
| derived, Hall | C5×C132 ⋊ C4×C9 |
| Hall | C5×#13095200 ⋊ C4 |
| Hall | C132×Dic5 ⋊ C9 |
| Sylow | C132 ⋊ C9×Dic5 |
| Sylow | C5 ⋊ C4×#13095200 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D5×#92788 |
| commutator, hypocenter | C5×C132 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C132 | C2×C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C2×C3 | |
288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30420 |
1416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 182);