Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | C4×C8×C13 ⋊ C4 |
| Sylow | C13 ⋊ #1744 |
296 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 126 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=d,e^2=g,b^a=bd,h^b=h^8,h^f=h^12176 conjugacy classes — view the full character table.
| maximal subgroup of | #16777096, #16777099, C8×#88100, … |
| maximal normal subgroup of | #16777096, #16777099, C8×#88100, … |
| maximal quotient of | #16780280, #16780281, #16780284, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20223);