Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#66694 |
| Fitting | C22×C32×C7 ⋊ C22 |
| Hall | C32×C7 ⋊ C2×D4 |
| Sylow | C32 ⋊ D4×D7 |
| Sylow | C7 ⋊ C3×D3×D4 |
232 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | #72246592, C3×D3×D4×D7, D3×#66694, … |
| maximal normal subgroup of | #72246592, C3×D3×D4×D7, D3×#66694, … |
| maximal quotient of | C3×#10621139, C3×#10621134 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 725);