Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C17×#108 ⋊ C8 |
| Sylow | C17 ⋊ #8294 |
358 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^8,17|a^2=e,b^2=f,c^2=de,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=cg,i^a=i^8,d^b=dg,e^b=eg,i^c=i^9,i^e=i^13,i^h=i^16116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1116881);