Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C13×M16 ⋊ C2 |
| Sylow | C13 ⋊ #2875 |
556 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=f,e^2=g,b^a=bg,h^a=h^12,d^c=dg,h^d=h^12308 conjugacy classes — view the full character table.
| maximal subgroup of | #15759729, #15759733, #15759736, … |
| maximal normal subgroup of | #15759729, #15759733, #15759736, … |
| maximal quotient of | #15828513, #15828534, #15828593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12939);