Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of C7⋊(C7⋊AGL(1,𝔽5)) |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊(C7⋊#170) |
| derived, Hall | C5×C72 ⋊ C8 |
| Sylow | C72 ⋊ #170 |
| Sylow | C5 ⋊ C7⋊(C7⋊C8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊(C7⋊AGL(1,𝔽5)) |
| commutator, hypocenter | C5×C72 | C8 |
| Fitting, socle, prime radical | C2×C5×C72 | C4 |
| cosocle | C72×Dic5 | C2 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C2 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1960 |
Polycyclic presentation:
2^3,5,7^2|a^2=b,b^2=c,d^a=d^2,e^a=e^6,f^a=f^6,d^b=d^4202 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 50);