Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C67×#1713 ⋊ C2 |
| Sylow | C67 ⋊ #20324 |
570 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 139 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=gh,b^2=gh,c^2=gh,e^2=g,f^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eg,f^a=fh,c^b=cgh,d^b=de,e^b=eg,i^b=i^66,f^c=fh,i^c=i^66,e^d=eg,i^d=i^661291 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 166881);