Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #2396 |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^c=h^12284 conjugacy classes — view the full character table.
| maximal subgroup of | #15758006, #15758008, #15758011, … |
| maximal normal subgroup of | #15758006, #15758008, #15758011, … |
| maximal quotient of | #15784629, #15784642, #15784663, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7778);