Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C13×D8 ⋊ C2 |
| Sylow | C13 ⋊ #3122 |
418 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^12,f^c=fg200 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3122, C2×#13125076, #16731285, … |
| maximal normal subgroup of | D13×#3122, C2×#13125076, #16731285, … |
| maximal quotient of | #15863007, #15866006, #15866016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14750);