Finite Group DatabasebetaFinite Group Databasebeta| order | 756 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×D7×H(3,𝔽3) |
| Fitting | C2×C7×H(3,𝔽3) ⋊ C2 |
| Hall | C7×H(3,𝔽3) ⋊ C22 |
| Sylow | C7 ⋊ C22×H(3,𝔽3) |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | D7×(C3⋊Dic3)⋊C3, #13094345, #13094346, … |
| maximal normal subgroup of | D7×(C3⋊Dic3)⋊C3, #13094345, #13094346, … |
| maximal quotient of | H(3,𝔽3)×Dic14, C4×D7×H(3,𝔽3), H(3,𝔽3)×D28, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(756, 119);