Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C13×#449 ⋊ C2 |
| Sylow | C13 ⋊ #3008 |
784 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,e^b=eg,d^c=dg,h^c=h^12,h^d=h^12146 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3008, C2×#13124101, #16729382, … |
| maximal normal subgroup of | D13×#3008, C2×#13124101, #16729382, … |
| maximal quotient of | #15836076, #15836078, #15836164, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13775);