Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C277 ⋊ #456 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4432 |
Polycyclic presentation:
2^6,277|a^2=f,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^276,d^b=df,e^b=ef,d^c=df2362 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47985186, #47985187, #47985191, … |
| maximal normal subgroup of | #47985186, #47985187, #47985191, … |
| maximal quotient of | #47982130, #47982136, #47982141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 732);