Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#11719541 |
| Fitting | C2×C13×H(5,𝔽2) ⋊ C2 |
| Sylow | C13 ⋊ C2×#577 |
1460 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | #15878829, #15878835, #15878856, … |
| maximal normal subgroup of | #15878829, #15878835, #15878856, … |
| maximal quotient of | C2×#13123362, C2×#13123366, C2×#13123429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19270);