Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| isoclinism | isoclinic class of C7⋊#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#6016 |
| derived, Hall | C7×C25 ⋊ C8 |
| Sylow | C25 ⋊ C7⋊C8 |
| Sylow | C7 ⋊ #6016 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C7⋊#1035 |
| commutator, hypocenter | C7×C25 | C8 |
| Frattini | C2×C5 | C7⋊AGL(1,𝔽5) |
| Fitting | C2×C7×C25 | C4 |
| socle, prime radical | C2×C5×C7 | AGL(1,𝔽5) |
| cosocle | C7×Dic25 | C2 |
| LCS | G ▷ C7×C25 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 1400 |
Polycyclic presentation:
2^3,5,7,5|a^2=b,b^2=c,d^5=f,d^a=d^2f,e^a=e^6,f^a=f^2,d^b=d^4f^4,f^b=f^4104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 6);