Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C67 ⋊ #10669 |
296 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4288 |
Polycyclic presentation:
2^8,67|a^2=dg,b^2=de,c^2=g,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,f^a=fgh,c^b=cf,d^b=dg,e^b=eg,f^b=fg,i^b=i^66,d^c=dh,e^c=eh,f^c=fg,i^c=i^661492 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 74594);