Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D63 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C9⋊C16) |
| unambiguous semidirect product | C9⋊(C7⋊C16) |
| derived, Hall | C7×C9 ⋊ C16 |
| Sylow | C9 ⋊ C7⋊C16 |
| Sylow | C7 ⋊ C9⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D63 |
| commutator, hypocenter | C7×C9 | C16 |
| Frattini | C3×C8 | D21 |
| Fitting, cosocle | C7×C8×C9 | C2 |
| socle, prime radical | C2×C3×C7 | C3⋊C8 |
| LCS | G ▷ C7×C9 | |
| UCS | C1 ◁ C8 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 1008 |
Polycyclic presentation:
2^4,3,7,3|a^2=b,b^2=c,c^2=d,e^3=g,e^a=e^2g^2,f^a=f^6,g^a=g^2264 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 5);