Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#376 ⋊ C2 |
| Sylow | C13 ⋊ #2398 |
568 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 157 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=e,b^2=e,d^2=ef,b^a=be,c^a=cf,c^b=cg,h^b=h^12,h^c=h^12284 conjugacy classes — view the full character table.
| maximal subgroup of | #15757987, #15758002, #15763765, … |
| maximal normal subgroup of | #15757987, #15758002, #15763765, … |
| maximal quotient of | #15784614, #15784655, #15784671, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7796);