Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C22×C42×C13 ⋊ C2 |
| Sylow | C13 ⋊ #2853 |
582 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 165 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|b^2=f,d^2=e,b^a=be,c^a=cf,d^a=dg,h^a=h^12428 conjugacy classes — view the full character table.
| maximal subgroup of | #15896159, #15896162, #15896783, … |
| maximal normal subgroup of | #15896159, #15896162, #15896783, … |
| maximal quotient of | #15794097, #15794141, #15794152, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12832);