Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic9⋊Dic7 |
| Hall | C7×C9 ⋊ C4⋊C4 |
| Sylow | C9 ⋊ C4⋊Dic7 |
| Sylow | C7 ⋊ Dic9⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D7×D9 |
| commutator | C2×C7×C9 | C2×C4 |
| Frattini | C22×C3 | D3×D7 |
| Fitting, cosocle | C22×C7×C9 | C22 |
| socle, prime radical | C22×C3×C7 | C2×D3 |
| hypocenter | C7×C9 | C4⋊C4 |
| LCS | G ▷ C2×C7×C9 ▷ C7×C9 | |
| UCS | C1 ◁ C22 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1008 |
Polycyclic presentation:
2^4,3,7,3|a^2=d,b^2=c,e^3=g,b^a=bc,f^a=f^6,e^b=e^2g^2,g^b=g^2114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 43);