Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×D8×C269 ⋊ C2 |
| Sylow | C269 ⋊ #459 |
140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 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|b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^268,e^c=ef1895 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #459×D269, C2×#31770798, #46820336, … |
| maximal normal subgroup of | #459×D269, C2×#31770798, #46820336, … |
| maximal quotient of | #46810224, #46810228, #46810238, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 742);