Finite Group DatabasebetaFinite Group Databasebeta| order | 756 |
| isoclinism | isoclinic class of #67355 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#67355 |
| Fitting | C2×C7×C9 ⋊ C2×C3 |
| Hall | #4428 ⋊ C22 |
| Hall | C2×D7 ⋊ 3−1+2 |
| Sylow | C7 ⋊ C22×3−1+2 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
62 conjugacy classes — view the full character table.
| maximal subgroup of | #67355⋊C4, #13094216, #13094219, … |
| maximal normal subgroup of | #67355⋊C4, #13094216, #13094219, … |
| maximal quotient of | #13094245, C4×#67355, C4⋊#67355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(756, 71);