Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #1289 |
228 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 77 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=e,c^2=fg,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^12,d^b=dg272 conjugacy classes — view the full character table.
| maximal subgroup of | #15749592, #15749593, #15749595, … |
| maximal normal subgroup of | #15749592, #15749593, #15749595, … |
| maximal quotient of | #15749457, #15749468, #15749497, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2378);