Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D8×C269 ⋊ C2 |
| Sylow | C269 ⋊ #576 |
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|e^2=f,b^a=be,e^a=ef,e^b=ef,d^c=df,g^d=g^2681898 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46812841, #46812845, #46812855, … |
| maximal normal subgroup of | #46812841, #46812845, #46812855, … |
| maximal quotient of | #46819406, #46819481, #46819710, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1350);