Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C269 ⋊ #389 |
170 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 17216 |
Polycyclic presentation:
2^6,269|a^2=f,b^2=f,c^2=e,b^a=bd,c^a=ce,g^a=g^2684316 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46808707, #46808709, #46811132, … |
| maximal normal subgroup of | #46808707, #46808709, #46811132, … |
| maximal quotient of | #46809115, #46809118, #46809137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 447);