Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C13 ⋊ #3501 |
1100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=g,c^2=g,b^a=bf,c^a=cg,e^a=ef,h^a=h^12,d^b=df284 conjugacy classes — view the full character table.
| maximal subgroup of | #15754454, #15754457, #15754476, … |
| maximal normal subgroup of | #15754454, #15754457, #15754476, … |
| maximal quotient of | #16023010, #16023347, #16023359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 18313);