Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C67×#1295 ⋊ C2 |
| Sylow | C67 ⋊ #8028 |
778 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 183 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=e,b^2=f,c^2=g,d^2=g,f^2=h,b^a=bd,d^a=dg,f^a=fgh,d^b=dh,i^c=i^661330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 59617);