Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#388 ⋊ C2 |
| Sylow | C13 ⋊ #2359 |
652 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=g,c^2=e,b^a=be,c^a=cf,d^b=de,h^b=h^12,h^c=h^12,h^d=h^12218 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2359, C2×#13117827, #16022483, … |
| maximal normal subgroup of | D13×#2359, C2×#13117827, #16022483, … |
| maximal quotient of | #15784325, #15784413, #15784431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7501);