Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C13×#121 ⋊ C2 |
| Sylow | C13 ⋊ #3188 |
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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|b^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^12,c^b=ce,f^c=fg200 conjugacy classes — view the full character table.
| maximal subgroup of | #15759398, #15759404, #15836797, … |
| maximal normal subgroup of | #15759398, #15759404, #15836797, … |
| maximal quotient of | #15871947, #15871957, #15873196, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 15275);