Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C277 ⋊ #543 |
242 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4432 |
Polycyclic presentation:
2^6,277|a^2=f,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,g^c=g^2762782 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982089, #47982092, #47982123, … |
| maximal normal subgroup of | #47982089, #47982092, #47982123, … |
| maximal quotient of | #47985779, #47985781, #47985895, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1175);