Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #107×C269 ⋊ C2 |
| Sylow | C269 ⋊ #357 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=d,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,c^b=ce,e^b=ef,g^b=g^2681898 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #357×D269, C2×#31770405, #46812590, … |
| maximal normal subgroup of | #357×D269, C2×#31770405, #46812590, … |
| maximal quotient of | #46808845, #46808893, #46808930, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 349);