Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ #1336 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=d,c^2=e,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^12,c^b=ceg,d^b=dg,e^b=eg200 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1336, C2×#13112812, #15772712, … |
| maximal normal subgroup of | D13×#1336, C2×#13112812, #15772712, … |
| maximal quotient of | #15749574, #15749577, #15749580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2486);