Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C8×C109 ⋊ C2 |
| Sylow | C109 ⋊ #448 |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^108,d^b=df,g^b=g^1081099 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28361985, #28361986, #28361997, … |
| maximal normal subgroup of | #28361985, #28361986, #28361997, … |
| maximal quotient of | #28361957, #28361974, #28362025, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 690);