Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C13×#518 ⋊ C2 |
| Sylow | C13 ⋊ #2883 |
800 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 249 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=f,b^a=be,e^a=eg,f^b=fg,h^b=h^12,d^c=dg245 conjugacy classes — view the full character table.
| maximal subgroup of | #15872066, #15872068, #15872072, … |
| maximal normal subgroup of | #15872066, #15872068, #15872072, … |
| maximal quotient of | #15828735, #15828741, #15828822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12970);