Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ #1445 |
520 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=de,c^2=de,b^a=bd,c^a=ce,h^a=h^12,c^b=cf284 conjugacy classes — view the full character table.
| maximal subgroup of | #15750241, #15755051, #15755053, … |
| maximal normal subgroup of | #15750241, #15755051, #15755053, … |
| maximal quotient of | #15750843, #15750846, #15771649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2778);