Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #107×C269 ⋊ C2 |
| Sylow | C269 ⋊ #480 |
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 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|c^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^268,g^b=g^268,e^c=ef1895 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #480×D269, C2×#31770920, #46820802, … |
| maximal normal subgroup of | #480×D269, C2×#31770920, #46820802, … |
| maximal quotient of | #46810970, #46811071, #46811201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 864);