Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | SD16×C22⋊D13 |
| Fitting | C22×C13×SD16 ⋊ C2 |
| Sylow | C13 ⋊ D4×SD16 |
546 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
203 conjugacy classes — view the full character table.
| maximal subgroup of | D4×SD16×D13, C2×SD16×C22⋊D13, #16738208, … |
| maximal normal subgroup of | D4×SD16×D13, C2×SD16×C22⋊D13, #16738208, … |
| maximal quotient of | #15852382, #15852387, #15852397, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 16200);