Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊#16810012) |
| Fitting, socle, derived, Hall | C32×C5×C132 ⋊ C4 |
| Hall | C32×C132 ⋊ Dic5 |
| Hall | C5×C132 ⋊ C3⋊Dic3 |
| Sylow | C132 ⋊ C3⋊Dic15 |
| Hall | C32×C5 ⋊ #10621730 |
| Sylow | C32 ⋊ #16810012 |
| Sylow | C5 ⋊ C3⋊(C3⋊#10621730) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C132 | C4 |
| prime radical, cosocle | C32×C5×C13×D13 | C2 |
| LCS | G ▷ C32×C5×C132 | |
| UCS | C1 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2340 |
Polycyclic presentation:
2^2,3^2,5,13^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^4,f^a=f^5,g^a=g^12,f^b=f^122343 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 903);