Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #66567⋊C3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ SD16 |
| Sylow | C7 ⋊ C3×#204 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^2,3,2^2,3,7|a^2=d,d^2=e,b^a=bde,g^a=g^6,d^b=de,f^b=f^2,g^c=g^254 conjugacy classes — view the full character table.
| maximal subgroup of | #72245516, AGL(1,𝔽7)×#204, #72245527, … |
| maximal normal subgroup of | #72245516, AGL(1,𝔽7)×#204, #72245527, … |
| maximal quotient of | #72254183 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 230);