Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊Dic491 |
| 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 | #44536491, #44536492, C4×C22⋊Dic491, … |
| maximal normal subgroup of | #44536491, #44536492, C4×C22⋊Dic491, … |
| maximal quotient of | C2×C491⋊#95, C4×C22⋊Dic491, #44536581, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 98);