Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C32×C269 ⋊ C2 |
| Sylow | C269 ⋊ SD64 |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^268,c^b=cd,d^b=de,e^b=ef,g^b=g^2684307 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD64×D269, C2×#31770444, #46813193, … |
| maximal normal subgroup of | SD64×D269, C2×#31770444, #46813193, … |
| maximal quotient of | #46809064, #46809067, #46809087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 388);