Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #2962 |
356 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=e,c^2=ef,f^2=g,b^a=be,h^a=h^5,d^c=dg,h^c=h^8,h^d=h^12,h^f=h^1292 conjugacy classes — view the full character table.
| maximal subgroup of | #16782689, #16782691, #16782697, … |
| maximal normal subgroup of | #16782689, #16782691, #16782697, … |
| maximal quotient of | #16797152, #16797162, #16797466, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21306);