Finite Group DatabasebetaFinite Group Databasebeta| order | 756 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×D7×3−1+2 |
| Fitting | C2×C7×3−1+2 ⋊ C2 |
| Hall | C7×3−1+2 ⋊ C22 |
| Sylow | C7 ⋊ C22×3−1+2 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | D7×3−1+2⋊C4, #13094352, #13094353, … |
| maximal normal subgroup of | D7×3−1+2⋊C4, #13094352, #13094353, … |
| maximal quotient of | 3−1+2×Dic14, C4×D7×3−1+2, 3−1+2×D28, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(756, 120);