Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#21463313 |
| Fitting | C2×D4×C491 ⋊ C2 |
| Sylow | C491 ⋊ C2×D8 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
2464 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536805, C4×#21463313, #44536834, … |
| maximal normal subgroup of | #44536805, C4×#21463313, #44536834, … |
| maximal quotient of | C2×#30628257, C2×#30628258, C2×#30628270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 156);