Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| unambiguous semidirect product | D13⋊#431 |
| Sylow | C13 ⋊ C2×#431 |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=e,f^2=g,b^a=be,h^a=h^8,h^d=h^12,h^f=h^12176 conjugacy classes — view the full character table.
| maximal subgroup of | #16778909, #16778911, #16778912, … |
| maximal normal subgroup of | #16778909, #16778911, #16778912, … |
| maximal quotient of | #16796834, C4×D13⋊(C22⋊C8), C4×D13⋊(C4⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21174);