Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C7⋊C9)⋊C16 |
| unambiguous semidirect product | (C7⋊C16)⋊C9 |
| derived, Sylow | C7 ⋊ C9×C16 |
| Hall | C7⋊C16 ⋊ C9 |
| Hall | C7⋊C9 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3×C8 | AGL(1,𝔽7) |
| commutator, hypocenter | C7 | C9×C16 |
| Fitting, cosocle | C3×C7×C8 | C2×C3 |
| socle, prime radical | C2×C3×C7 | C3×C8 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C3×C8 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1008 |
Polycyclic presentation:
2,3,2,3,2^2,7|a^2=c,b^3=d,c^2=e,e^2=f,g^a=g^6,g^b=g^4168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 1);