Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×C8×C13 ⋊ C2 |
| Sylow | C13 ⋊ #3168 |
380 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|b^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^12428 conjugacy classes — view the full character table.
| maximal subgroup of | #15772901, #15772904, #15772906, … |
| maximal normal subgroup of | #15772901, #15772904, #15772906, … |
| maximal quotient of | #15863466, #15867128, #15867138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 15080);