Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C277 ⋊ #334 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
Polycyclic presentation:
2^6,277|a^2=d,b^2=c,c^2=e,d^2=f,b^a=bc,c^a=ce,g^b=g^2762788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #334×D277, C2×#31799752, #47981913, … |
| maximal normal subgroup of | #334×D277, C2×#31799752, #47981913, … |
| maximal quotient of | #47981001, #47981230, #47981232, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 299);