Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C13 |
No aliases for this group.
| derived, Hall | C5×#13095201 ⋊ C4 |
| Hall | #13095201 ⋊ AGL(1,𝔽5) |
| Hall | C5×C132 ⋊ Dic9 |
| Sylow | C132 ⋊ C9⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ #20258785 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C5×#13095201 | C4 |
| Frattini | C3 | #23778486 |
| Fitting, socle | C3×C5×C132 | Dic3 |
| prime radical | C3×C5⋊(C13⋊D13) | D3 |
| cosocle | C5⋊#15690149 | C2 |
| LCS | G ▷ C5×#13095201 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 585 |
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=f,f^a=e^12,g^a=g^2,d^b=d^4,e^b=e^12,f^b=f^12,e^c=e^3,f^c=f^9231 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 257);