Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C13×#101 ⋊ C4 |
| Sylow | C13 ⋊ #1757 |
284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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=e,b^2=f,c^2=e,e^2=g,b^a=bd,f^a=fg,h^a=h^5,d^b=dg,h^b=h^5,h^c=h^8,h^e=h^12,h^f=h^1277 conjugacy classes — view the full character table.
| maximal subgroup of | #16789478, #16789482, #16789486, … |
| maximal normal subgroup of | #16789478, #16789482, #16789486, … |
| maximal quotient of | #16780384, #16780390, #16780392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20269);