Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C269 ⋊ #356 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=f,c^2=f,d^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^268,c^b=cf,d^b=def,d^c=df1889 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46809039, #46809040, #46809051, … |
| maximal normal subgroup of | #46809039, #46809040, #46809051, … |
| maximal quotient of | #46808819, #46808831, #46808891, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 348);