Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#21463312 |
| Sylow | C491 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
3940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536481, C491⋊#338, #44536484, … |
| maximal normal subgroup of | #44536481, C491⋊#338, #44536484, … |
| maximal quotient of | C2×#30628248, C4×#21463312, C2×C22⋊(C491⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 151);