Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×#11718234 |
| Fitting | C2×C42×C13 ⋊ C4 |
| Sylow | C13 ⋊ C2×#339 |
488 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#339, C4×#11718234, #16785205, … |
| maximal normal subgroup of | #261×#339, C4×#11718234, #16785205, … |
| maximal quotient of | C2×#13129664, #16778967, #16778974, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20187);