Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C16×C269 ⋊ C2 |
| Sylow | C269 ⋊ #504 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=d,d^2=e,e^2=f,c^b=cf,g^c=g^2684328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46809026, #46809028, #46812720, … |
| maximal normal subgroup of | #46809026, #46809028, #46812720, … |
| maximal quotient of | #46812480, #46812481, #46812497, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 965);