Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C67 ⋊ #14688 |
1422 conjugacy classes of subgroups; only the 443 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 443 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 17152 |
Polycyclic presentation:
2^8,67|a^2=h,b^2=eg,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=dg,i^c=i^661936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 100762);