Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ #23840 |
662 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 211 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4352 |
Polycyclic presentation:
2^8,17|a^2=eh,b^2=e,c^2=e,d^2=ef,g^2=h,b^a=be,c^a=cf,c^b=cg,d^b=dh,g^b=gh,i^b=i^16,g^c=gh,i^c=i^16500 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 200506);