Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #1770 |
272 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 114 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=e,b^2=f,c^2=de,e^2=g,b^a=bd,h^a=h^8,c^b=cg,h^c=h^8,h^e=h^12116 conjugacy classes — view the full character table.
| maximal subgroup of | #16780826, #16780831, #16780836, … |
| maximal normal subgroup of | #16780826, #16780831, #16780836, … |
| maximal quotient of | #16780858, #16780863, #16780882, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20305);