Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #127×C269 ⋊ C2 |
| Sylow | C269 ⋊ #459 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,e^c=ef,g^c=g^2681895 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46809937, #46809938, #46809947, … |
| maximal normal subgroup of | #46809937, #46809938, #46809947, … |
| maximal quotient of | #46810223, #46810237, #46810247, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 741);