Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C13 ⋊ #1274 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=e,c^2=f,d^2=g,b^a=bc,e^a=ef,h^a=h^12,d^b=df284 conjugacy classes — view the full character table.
| maximal subgroup of | #15749694, #15749695, #15749732, … |
| maximal normal subgroup of | #15749694, #15749695, #15749732, … |
| maximal quotient of | #15749445, #15749451, #15749453, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2339);