Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C13×M64 ⋊ C2 |
| Sylow | C13 ⋊ #1400 |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,d^b=dg,h^b=h^12284 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1400, C2×#13112975, #15783121, … |
| maximal normal subgroup of | D13×#1400, C2×#13112975, #15783121, … |
| maximal quotient of | #15750257, #15750317, #15750359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2649);