Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #3084 |
376 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=eg,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^12,f^c=fg200 conjugacy classes — view the full character table.
| maximal subgroup of | #15920459, #15920462, #15920468, … |
| maximal normal subgroup of | #15920459, #15920462, #15920468, … |
| maximal quotient of | #15862444, #15863921, #15863963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14370);