Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C43×C13 ⋊ C2 |
| Sylow | C13 ⋊ #2298 |
524 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 205 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=g,b^2=g,c^2=e,d^2=f,b^a=be,c^a=cf,h^a=h^12440 conjugacy classes — view the full character table.
| maximal subgroup of | #15756370, #15756374, #15861143, … |
| maximal normal subgroup of | #15756370, #15756374, #15861143, … |
| maximal quotient of | #15784039, #15784050, #15784061, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7007);