Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M16×C269 ⋊ C2 |
| Sylow | C269 ⋊ #568 |
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 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|a^2=e,e^2=f,d^a=df,c^b=cf,g^c=g^2682714 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46811103, #46811106, #46811122, … |
| maximal normal subgroup of | #46811103, #46811106, #46811122, … |
| maximal quotient of | #46819302, #46819303, #46819310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1315);