Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×M16×D13 |
| Fitting | C4×C13×M16 ⋊ C2 |
| Sylow | C13 ⋊ C2×C4×M16 |
656 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×#1278, #15752413, #15752433, … |
| maximal normal subgroup of | D13×#1278, #15752413, #15752433, … |
| maximal quotient of | C8×M16×D13, D13×#1451, D13×#1453, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12915);