Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C67×#2062 ⋊ C2 |
| Sylow | C67 ⋊ #23598 |
1200 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 173 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|c^2=h,d^2=e,b^a=be,c^a=cf,g^a=gh,i^a=i^66,c^b=cg,f^b=fh,i^b=i^66,d^c=dh,i^c=i^66,i^d=i^66904 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 198095);