Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C109 ⋊ #456 |
142 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=f,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^108,d^b=df,e^b=ef,d^c=df934 conjugacy classes — view the full character table.
| maximal subgroup of | #28365051, #28365052, #28365056, … |
| maximal normal subgroup of | #28365051, #28365052, #28365056, … |
| maximal quotient of | #28361995, #28362001, #28362006, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 732);