Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #3095 |
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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=g,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^12,f^c=fg,h^c=h^12200 conjugacy classes — view the full character table.
| maximal subgroup of | #15759974, #15759976, #15760086, … |
| maximal normal subgroup of | #15759974, #15759976, #15760086, … |
| maximal quotient of | #15862731, #15863669, #15864159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14459);