Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #131×C109 ⋊ C2 |
| Sylow | C109 ⋊ #471 |
104 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,109|b^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^108,e^c=ef1096 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #471×D109, C2×#20295289, #28372747, … |
| maximal normal subgroup of | #471×D109, C2×#20295289, #28372747, … |
| maximal quotient of | #28362373, #28362380, #28362407, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 812);