Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C13 ⋊ #2888 |
756 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=f,f^2=g,b^a=be,e^a=eg,h^a=h^8,f^b=fg,d^c=dg,h^f=h^12101 conjugacy classes — view the full character table.
| maximal subgroup of | #16790644, #16790646, #16790652, … |
| maximal normal subgroup of | #16790644, #16790646, #16790652, … |
| maximal quotient of | #16792821, #16792822, #16792824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21120);