Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C269 ⋊ #543 |
242 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|a^2=f,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,g^c=g^2682702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46809807, #46809810, #46809841, … |
| maximal normal subgroup of | #46809807, #46809810, #46809841, … |
| maximal quotient of | #46813497, #46813499, #46813613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1175);