Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C269 ⋊ #461 |
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=f,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^268,e^c=ef1895 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #461×D269, C2×#31770808, #46820336, … |
| maximal normal subgroup of | #461×D269, C2×#31770808, #46820336, … |
| maximal quotient of | #46810258, #46810262, #46810272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 752);