Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C269 ⋊ #510 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|b^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,d^b=de,e^b=ef,g^b=g^2681892 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46812773, #46812776, #46812836, … |
| maximal normal subgroup of | #46812773, #46812776, #46812836, … |
| maximal quotient of | #46812597, #46812604, #46812674, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 989);