Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C13×C22⋊C4 ⋊ C2 |
| Sylow | C13 ⋊ #2353 |
588 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=f,c^2=ef,b^a=be,c^a=cf,h^a=h^12,d^b=de,h^b=h^12,h^d=h^12290 conjugacy classes — view the full character table.
| maximal subgroup of | #15756544, #15756549, #15830637, … |
| maximal normal subgroup of | #15756544, #15756549, #15830637, … |
| maximal quotient of | #15784353, #15784374, #15784384, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7453);