Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | D3×Q8×ΓL(1,𝔽8) |
| Fitting | C3×C7×Q8 ⋊ C2×C3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×Q8 |
| Sylow | C7 ⋊ C3×D3×Q8 |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#41×ΓL(1,𝔽8), D3×Q8×AGL(1,𝔽7), D3×#66659, … |
| maximal normal subgroup of | D3×#41×ΓL(1,𝔽8), D3×Q8×AGL(1,𝔽7), D3×#66659, … |
| maximal quotient of | ΓL(1,𝔽8)×#3797 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 653);