Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#389 ⋊ C2 |
| Sylow | C13 ⋊ C4×C22⋊Q8 |
656 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=e,d^2=eg,b^a=be,c^a=cf,h^c=h^12,h^d=h^12224 conjugacy classes — view the full character table.
| maximal subgroup of | #15750880, #15750953, #15750983, … |
| maximal normal subgroup of | #15750880, #15750953, #15750983, … |
| maximal quotient of | #15784085, #15784093, Dic13×#389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7040);