Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C13×#376 ⋊ C2 |
| Sylow | C13 ⋊ #2401 |
432 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 141 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=fg,b^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^c=h^12284 conjugacy classes — view the full character table.
| maximal subgroup of | #15871173, #15871176, #15871180, … |
| maximal normal subgroup of | #15871173, #15871176, #15871180, … |
| maximal quotient of | #15784614, #15784642, #15784698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7808);