Finite Group DatabasebetaFinite Group Databasebeta| order | 756 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | #4427 ⋊ C4 |
| Hall | Dic7 ⋊ 3−1+2 |
| Sylow | C7 ⋊ C4×3−1+2 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
Polycyclic presentation:
2,3^2,2,3,7|a^2=d,c^3=e^2,f^a=f^6,c^b=ce,f^b=f^462 conjugacy classes — view the full character table.
| maximal subgroup of | #13094202, #67361⋊C4, #67366⋊C4, … |
| maximal normal subgroup of | #13094202, #67361⋊C4, #67366⋊C4, … |
| maximal quotient of | #13094147, C2×#10625387 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(756, 18);