Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C13 ⋊ #2880 |
774 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 204 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=f,f^2=g,b^a=be,h^a=h^8,h^b=h^12,d^c=dg,h^c=h^12,h^d=h^12,h^f=h^12110 conjugacy classes — view the full character table.
| maximal subgroup of | #16783792, #16783794, #16783800, … |
| maximal normal subgroup of | #16783792, #16783794, #16783800, … |
| maximal quotient of | #16793164, #16793172, #16793178, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21101);