Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C269 ⋊ C2 |
| Sylow | C269 ⋊ #399 |
186 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 61 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=d,b^2=de,b^a=bd,c^a=ce,c^b=cf,g^c=g^2682702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46809903, #46809908, #46809930, … |
| maximal normal subgroup of | #46809903, #46809908, #46809930, … |
| maximal quotient of | #46809127, #46809129, #46809148, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 484);