Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of #13108193 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Hall | C5×#732 ⋊ C4 |
| Sylow | #732 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ #66332 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×#732 | C4 |
| Frattini | C32 | C3⋊ΓL(1,𝔽16) |
| socle | C3×C5 | #1084 |
| prime radical, cosocle | D5×#732 | C2 |
| LCS | G ▷ C5×#732 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
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=df,f^c=fg,f^d=fg^243 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#4185, #72247296, #72268714, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#4185, #72247296, #72268714, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 99);