Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C13×#423 ⋊ C2 |
| Sylow | C13 ⋊ #2925 |
392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=e,f^2=g,b^a=be,h^a=h^12,d^b=dg,h^b=h^12,d^c=dg,h^c=h^12218 conjugacy classes — view the full character table.
| maximal subgroup of | #15757223, #15757227, #15757237, … |
| maximal normal subgroup of | #15757223, #15757227, #15757237, … |
| maximal quotient of | #15860419, #15860473, #15860844, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13178);