Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C277 ⋊ #499 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
Polycyclic presentation:
2^6,277|a^2=d,b^2=df,c^2=e,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^2761954 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47985341, #47985342 |
| maximal normal subgroup of | #47985341, #47985342 |
| maximal quotient of | #47983328, #47983893, #47983896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 949);