Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C269 ⋊ C2 |
| Sylow | C269 ⋊ #577 |
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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=f,e^2=f,b^a=be,e^a=ef,g^a=g^268,e^b=ef,d^c=df2300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46822646, #46822649, #46822658, … |
| maximal normal subgroup of | #46822646, #46822649, #46822658, … |
| maximal quotient of | #46819411, #46819415, #46819478, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1360);