Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C13×C4⋊C4 ⋊ C2 |
| Sylow | C13 ⋊ #2275 |
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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=f,b^2=g,c^2=f,b^a=be,d^a=de,c^b=ce,h^c=h^12,h^d=h^12308 conjugacy classes — view the full character table.
| maximal subgroup of | #15759813, #15759817, #15759827, … |
| maximal normal subgroup of | #15759813, #15759817, #15759827, … |
| maximal quotient of | #15784000, #15784004, #15784197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6870);