Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C269 ⋊ #423 |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=e,b^2=d,e^2=f,b^a=bd,c^a=cf,g^b=g^2682708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46808835, #46810875, #46810876, … |
| maximal normal subgroup of | #46808835, #46810875, #46810876, … |
| maximal quotient of | #46809640, #46809643, #46809646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 572);