Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#126 ⋊ C4 |
| Sylow | C13 ⋊ #2373 |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=g,c^2=e,d^2=ef,b^a=be,c^a=cf,h^a=h^5,d^b=de,h^b=h^8,h^g=h^1292 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13131373, #16807611, #16807613, … |
| maximal normal subgroup of | C2×#13131373, #16807611, #16807613, … |
| maximal quotient of | #16791633, #16791646, #16791648, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21047);