Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×#100×C67 ⋊ C2 |
| Sylow | C67 ⋊ #25870 |
1370 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1370 conjugacy classes of subgroups — too many to draw. Only its 191 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|a^2=h,b^2=e,c^2=ef,d^2=e,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,g^a=gh,i^a=i^66,c^b=cg,f^b=fh,g^c=gh1495 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 225867);