Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#123 ⋊ C4 |
| Sylow | C13 ⋊ #2335 |
532 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=g,d^2=ef,b^a=be,c^a=cf,d^a=de,h^a=h^5,c^b=ce,h^b=h^8,h^g=h^1286 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13131335, #16807543, #16807544, … |
| maximal normal subgroup of | C2×#13131335, #16807543, #16807544, … |
| maximal quotient of | #16791573, #16791589, #16791591, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21009);