Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C9⋊#16810004 |
| Fitting, derived, Hall | C5×C9×C132 ⋊ C4 |
| Hall | C9×C132 ⋊ AGL(1,𝔽5) |
| Hall | C5×C132 ⋊ Dic9 |
| Sylow | C132 ⋊ C9⋊AGL(1,𝔽5) |
| Hall | C5×C9 ⋊ #10621729 |
| Sylow | C9 ⋊ #16810004 |
| Sylow | C5 ⋊ C9⋊#10621729 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C9×C132 | C4 |
| Frattini | C3 | C3⋊#16810004 |
| socle | C3×C5×C132 | Dic3 |
| prime radical | C3×C5⋊(C13⋊D13) | D3 |
| cosocle | C9×C5⋊(C13⋊D13) | C2 |
| LCS | G ▷ C5×C9×C132 | |
| UCS | C1 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1170 |
Polycyclic presentation:
2^2,3,5,13^2,3|a^2=b,c^3=g^2,c^a=c^2g,d^a=d^2,e^a=e^5,f^a=f^8,g^a=g^2,d^b=d^4,e^b=e^12,f^b=f^121911 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 346);