Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C269 ⋊ #452 |
152 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 47 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=f,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^268,d^b=df2699 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #452×D269, C2×#31770767, #46820100, … |
| maximal normal subgroup of | #452×D269, C2×#31770767, #46820100, … |
| maximal quotient of | #46809848, #46809865, #46809916, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 711);