Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C13×D16 ⋊ C2 |
| Sylow | C13 ⋊ #2263 |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,h^a=h^12,d^b=de,e^b=ef,f^b=fg158 conjugacy classes — view the full character table.
| maximal subgroup of | #15783542, #15783547, #15783590, … |
| maximal normal subgroup of | #15783542, #15783547, #15783590, … |
| maximal quotient of | #15783356, #15783362, #15783424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6823);