Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of C5⋊#87658 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C5⋊#87658 |
| Fitting, socle, Hall | C5×C72 ⋊ Q8 |
| Sylow | C72 ⋊ Dic10 |
| Sylow | C5 ⋊ #87658 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, prime radical, cosocle | C5×C7⋊D7 | C22 |
| Fitting, socle, hypocenter | C5×C72 | Q8 |
| LCS | G ▷ C5×C7⋊D7 ▷ C5×C72 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 140 |
Polycyclic presentation:
2^3,5,7^2|a^2=c,b^2=c,b^a=bc,d^a=d^4,e^a=e^3f^5,f^a=e^5f^4,e^b=e^4f^4,f^b=ef^3,e^c=e^6,f^c=f^643 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 125);