Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4×D4×C13 ⋊ C2 |
| Sylow | C13 ⋊ #2463 |
668 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^12278 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2463, C2×#13118827, #16030454, … |
| maximal normal subgroup of | D13×#2463, C2×#13118827, #16030454, … |
| maximal quotient of | #15785002, #15785008, #15785936, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 8501);