Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#11719089 |
| Fitting | C22×C8×C13 ⋊ C4 |
| Sylow | C13 ⋊ C2×#405 |
592 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #16785198, #16785199, #16785222, … |
| maximal normal subgroup of | #16785198, #16785199, #16785222, … |
| maximal quotient of | C2×C8×#6122, C8×D13⋊M16, C2×C8×#6118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21068);