Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C277 ⋊ #462 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
Polycyclic presentation:
2^6,277|a^2=f,b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^276,e^c=ef,g^c=g^2762779 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982354, #47982356, #47982361, … |
| maximal normal subgroup of | #47982354, #47982356, #47982361, … |
| maximal quotient of | #47982550, #47982562, #47982572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 760);