Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C13×#346 ⋊ C2 |
| Sylow | C13 ⋊ #2177 |
172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=e,c^2=eg,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,h^a=h^12,d^b=df,f^b=fg,h^b=h^12272 conjugacy classes — view the full character table.
| maximal subgroup of | #15750389, #15750391, #15774803, … |
| maximal normal subgroup of | #15750389, #15750391, #15774803, … |
| maximal quotient of | #15774671, #15774844, #15774928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6387);