Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ #33435 |
674 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^8,17|a^2=f,c^2=f,f^2=g,g^2=h,b^a=be,c^a=ch,d^a=dh,i^a=i^9,d^b=dh,i^b=i^16,i^c=i^9,i^d=i^16,i^f=i^13,i^g=i^16116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1118394);