Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C5×C132 ⋊ C4×C9 |
| Hall | C5×#13095200 ⋊ C4 |
| Hall | C13×#63121 ⋊ C9 |
| Hall | #13095200 ⋊ AGL(1,𝔽5) |
| Sylow | C132 ⋊ C9×AGL(1,𝔽5) |
| Sylow | C5 ⋊ #20258776 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #23778468 |
| commutator, hypocenter | C5×C132 | C4×C9 |
| Fitting, socle | C3×C5×C132 | C3×C4 |
| prime radical, cosocle | C3×C13×D65 | C2×C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C3 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2340 |
Polycyclic presentation:
2,3,2,5,13^2,3|a^2=c,b^3=g,d^a=d^2,e^a=e^8,e^b=e^3,f^b=f^3,d^c=d^4,e^c=e^12300 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 239);