Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #1386 |
140 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 73 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=f,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^12,c^b=cg,h^b=h^12200 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1386, C2×#13112943, #15777836, … |
| maximal normal subgroup of | D13×#1386, C2×#13112943, #15777836, … |
| maximal quotient of | #15749798, #15749847, #15749854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2617);