Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ #2988 |
432 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 297 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,d^2=e,f^2=g,b^a=be,d^a=de,h^a=h^12,c^b=ce308 conjugacy classes — view the full character table.
| maximal subgroup of | #15756800, #15756804, #15756807, … |
| maximal normal subgroup of | #15756800, #15756804, #15756807, … |
| maximal quotient of | #15861710, #15861808, #15861959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13621);