Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C269 ⋊ #383 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
Polycyclic presentation:
2^6,269|a^2=f,b^2=de,c^2=d,b^a=bd,c^a=ce,g^a=g^2684316 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46808750, #46808751, #46809432, … |
| maximal normal subgroup of | #46808750, #46808751, #46809432, … |
| maximal quotient of | #46809112, #46809147, #46811028, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 417);