Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C269 ⋊ #362 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=f,c^2=e,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^268,c^b=cef,d^b=df,e^b=ef,g^b=g^2682696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #362×D269, C2×#31770422, #46812631, … |
| maximal normal subgroup of | #362×D269, C2×#31770422, #46812631, … |
| maximal quotient of | #46808856, #46808904, #46808935, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 366);