Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C67 ⋊ #13522 |
240 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2144 |
Polycyclic presentation:
2^8,67|a^2=eg,b^2=d,c^2=d,d^2=h,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,c^b=cf,f^b=fh,e^c=eg,f^c=fh,g^c=gh,i^c=i^661486 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 89598);