Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #1451 |
208 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 98 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=d,b^2=e,d^2=f,e^2=g,b^a=bg,c^a=cf,h^b=h^8,h^e=h^12116 conjugacy classes — view the full character table.
| maximal subgroup of | #16780431, #16780432, #16780436, … |
| maximal normal subgroup of | #16780431, #16780432, #16780436, … |
| maximal quotient of | #16778870, #16778890, #16780283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19717);