Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C67×#1746 ⋊ C2 |
| Sylow | C67 ⋊ #22265 |
962 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 962 conjugacy classes of subgroups — too many to draw. Only its 227 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8576 |
Polycyclic presentation:
2^8,67|a^2=g,b^2=eg,c^2=ef,d^2=e,g^2=h,b^a=be,c^a=cf,d^a=deh,i^a=i^66,c^b=ceh,d^c=dh1900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 183318);