Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #2370 |
464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=fg,c^2=ef,d^2=e,b^a=be,c^a=cf,d^b=de,h^c=h^12290 conjugacy classes — view the full character table.
| maximal subgroup of | #15884765, #15884767, #15884780, … |
| maximal normal subgroup of | #15884765, #15884767, #15884780, … |
| maximal quotient of | #15784361, #15784465, #15784476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7602);