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^a=g^2764444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981134, #47981135, #47981137, … |
| maximal normal subgroup of | #47981134, #47981135, #47981137, … |
| maximal quotient of | #47981002, #47981231, #47981233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 300);