Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #1296 |
188 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=e,c^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^12,c^b=cg278 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1296, C2×#13112720, #15753004, … |
| maximal normal subgroup of | D13×#1296, C2×#13112720, #15753004, … |
| maximal quotient of | #15749471, #15749487, #15749488, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2394);