Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#21463311 |
| Fitting | C2×C8×C491 ⋊ C2 |
| 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 | #44536506, C4×#21463311, #44536677, … |
| maximal normal subgroup of | #44536506, C4×#21463311, #44536677, … |
| maximal quotient of | C2×#30628247, C4×#21463311, C2×(C2×D491)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 150);