Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C491⋊C8) |
| Sylow | C491 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15712 |
Polycyclic presentation:
2^5,491|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^4903940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊(C491⋊C8), #44536454, Q8⋊(C491⋊C8), … |
| maximal normal subgroup of | D4⋊(C491⋊C8), #44536454, Q8⋊(C491⋊C8), … |
| maximal quotient of | #44536476, #44536478, #44536480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 76);