Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #2028 |
246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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=d,b^2=d,c^2=g,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,c^b=cf,e^b=eg,h^b=h^12,e^c=eg,h^c=h^12194 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2028, C2×#13115996, #15890287, … |
| maximal normal subgroup of | D13×#2028, C2×#13115996, #15890287, … |
| maximal quotient of | #15765893, #15765898, #15765913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 5670);