Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#557 ⋊ C2 |
| Sylow | C13 ⋊ #3371 |
344 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|b^2=e,c^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^12,c^b=cg,d^b=de,f^c=fg179 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3371, C2×#13127604, #16742735, … |
| maximal normal subgroup of | D13×#3371, C2×#13127604, #16742735, … |
| maximal quotient of | #15879605, #15879799, #15881912, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17278);