Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C13×#127 ⋊ C4 |
| Sylow | C13 ⋊ #2380 |
648 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 152 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=g,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^8,c^b=cef,d^b=de,h^g=h^1280 conjugacy classes — view the full character table.
| maximal subgroup of | #16783977, #16783981, #16783982, … |
| maximal normal subgroup of | #16783977, #16783981, #16783982, … |
| maximal quotient of | #16791673, #16791677, #16792225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21054);