Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #3248 |
354 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^12,c^b=ce,f^c=fg200 conjugacy classes — view the full character table.
| maximal subgroup of | #15840117, #15840123, #15840132, … |
| maximal normal subgroup of | #15840117, #15840123, #15840132, … |
| maximal quotient of | #15872824, #15872834, #15873308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 15847);