Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C269 ⋊ #359 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=d,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^268,c^b=ce,e^b=ef1898 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #359×D269, C2×#31770412, #46812611, … |
| maximal normal subgroup of | #359×D269, C2×#31770412, #46812611, … |
| maximal quotient of | #46808846, #46808849, #46808900, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 356);