Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#11724784 |
| Sylow | C109 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^108,c^b=ce1108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C8×D109, C2×Q8⋊#11724784, #28361413, … |
| maximal normal subgroup of | Q8⋊C8×D109, C2×Q8⋊#11724784, #28361413, … |
| maximal quotient of | #28360855, #28360858, #28360873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 280);