Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of D5⋊#5997 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C7 |
| unambiguous semidirect product | D5⋊#5997 |
| unambiguous semidirect product | #11758266⋊C2 |
| Fitting, socle, derived, Hall | C5×C72 ⋊ C2×C4 |
| Sylow | C72 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C72 | C2×C4 |
| prime radical | D5×C7⋊D7 | C2 |
| cosocle | C5⋊(C7⋊D7) | C22 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 70 |
Polycyclic presentation:
2^3,5,7^2|a^2=c,d^a=d^2,e^a=e^3f^5,f^a=e^5f^4,d^b=d^4,d^c=d^4,e^c=e^6,f^c=f^658 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 119);