Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C8×Q8×C13 ⋊ C2 |
| Sylow | C13 ⋊ #2982 |
396 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,c^b=ce,h^d=h^12308 conjugacy classes — view the full character table.
| maximal subgroup of | #15832361, #15832363, #15832365, … |
| maximal normal subgroup of | #15832361, #15832363, #15832365, … |
| maximal quotient of | #15861647, #15861957, #15861958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13589);