Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×(C2×D491)⋊C4 |
| Fitting | C22×C4×C491 ⋊ C2 |
| Sylow | C491 ⋊ C2×C22⋊C4 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
3940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536448, #44536572, C4×(C2×D491)⋊C4, … |
| maximal normal subgroup of | #44536448, #44536572, C4×(C2×D491)⋊C4, … |
| maximal quotient of | C2×C491⋊#95, C4×(C2×D491)⋊C4, #44536580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 97);