Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of C5⋊#4183 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C5×AΣL(1,𝔽27) ⋊ C4 |
| Sylow | AΣL(1,𝔽27) ⋊ Dic5 |
| Sylow | C5 ⋊ #66330 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊#4183 |
| commutator, hypocenter | C5×AΣL(1,𝔽27) | C4 |
| Frattini | C2×C32 | C3⋊D15 |
| Fitting, prime radical, cosocle | C2×C5×AΣL(1,𝔽27) | C2 |
| socle | C2×C3×C5 | #272 |
| LCS | G ▷ C5×AΣL(1,𝔽27) | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2^2,3^2,5,3^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^4,f^a=fg^2,g^a=g^2,d^c=df,f^d=fg94 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 58);