Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C67 ⋊ #11416 |
228 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 123 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=d,b^2=e,d^2=f,e^2=g,g^2=h,b^a=bg,c^a=ch,e^a=eh,c^b=cf,d^b=dh,i^b=i^662704 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 78623);