Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D3×ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×D3×ΓL(1,𝔽8) |
| unambiguous semidirect product | (C2×C4×D3×C7)⋊C3 |
| Fitting | C2×C3×C4×C7 ⋊ C2×C3 |
| derived | C3×C7 ⋊ C22×C3×C4 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C22×C4 |
| Sylow | C7 ⋊ C2×C3×C4×D3 |
232 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 648);