Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Fitting | C67×#1713 ⋊ C2 |
| Sylow | C67 ⋊ #12512 |
268 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 79 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|b^2=dg,c^2=ef,d^2=fh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,g^a=gh,i^a=i^66,c^b=ch,i^b=i^66,i^c=i^661300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 84269);