Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#14555660 |
| Sylow | C277 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
Polycyclic presentation:
2^6,277|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^276,c^b=ce2788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C8×D277, C2×Q8⋊#14555660, #47981548, … |
| maximal normal subgroup of | Q8⋊C8×D277, C2×Q8⋊#14555660, #47981548, … |
| maximal quotient of | #47980990, #47980993, #47981008, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 280);