Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #1290 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=e,c^2=fg,d^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^12,d^b=dg272 conjugacy classes — view the full character table.
| maximal subgroup of | #15749604, #15749605, #15749607, … |
| maximal normal subgroup of | #15749604, #15749605, #15749607, … |
| maximal quotient of | #15749457, #15749465, #15749506, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2380);