Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C109 ⋊ #428 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,c^b=cf,g^b=g^1081102 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28363240, #28363241, #28363245, … |
| maximal normal subgroup of | #28363240, #28363241, #28363245, … |
| maximal quotient of | #28361782, #28361797, #28361815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 589);