Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of #13108191 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C5×AΣL(1,𝔽27) ⋊ C4 |
| Sylow | AΣL(1,𝔽27) ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ #66330 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×AΣL(1,𝔽27) | C4 |
| Frattini | C32 | C3⋊ΓL(1,𝔽16) |
| socle | C3×C5 | #1084 |
| prime radical, cosocle | D5×AΣL(1,𝔽27) | C2 |
| LCS | G ▷ C5×AΣL(1,𝔽27) | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
Polycyclic presentation:
2^2,3^2,5,3^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,g^a=g^2,e^b=e^4,d^c=dfg,f^d=fg^243 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#4183, C3×#13108191, #72247271 |
| maximal normal subgroup of | AGL(1,𝔽5)×#4183, C3×#13108191, #72247271 |
| maximal quotient of | C3×#13108191 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 97);