Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#463 ⋊ C2 |
| Sylow | C13 ⋊ #3264 |
568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^12,d^b=de,e^b=eg,h^b=h^12,h^c=h^12,e^d=eg143 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3264, C2×#13126322, #16737993, … |
| maximal normal subgroup of | D13×#3264, C2×#13126322, #16737993, … |
| maximal quotient of | #15852272, #15852392, #15852512, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 15996);