Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| 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,g^a=g^268,c^b=cf2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46812719, #46812722, #46812724, … |
| maximal normal subgroup of | #46812719, #46812722, #46812724, … |
| maximal quotient of | #46812482, #46812499, #46812644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 966);