Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #2047 |
256 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 69 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=g,b^2=g,c^2=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^12,c^b=cf,d^b=dg,h^b=h^12,e^c=eg,f^c=fg194 conjugacy classes — view the full character table.
| maximal subgroup of | #15775411, #15775413, #15775416, … |
| maximal normal subgroup of | #15775411, #15775413, #15775416, … |
| maximal quotient of | #15766529, #15766536, #15766585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 5778);