Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×D7×#67 |
| Fitting | C22×C32×C7 ⋊ C22 |
| Hall | C32×C7 ⋊ C2×D4 |
| Sylow | C32 ⋊ D4×D7 |
| Sylow | C7 ⋊ C2×C3×#67 |
248 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 84 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67×AGL(1,𝔽7), D7×#3811, C3×#72222120, … |
| maximal normal subgroup of | C3×#67×AGL(1,𝔽7), D7×#3811, C3×D7×#235, … |
| maximal quotient of | C3×#72222120, C3×D7×#214, C3×D7×#213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 723);