Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C491 ⋊ #108 |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
Polycyclic presentation:
2^5,491|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^4903934 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536532, #44536533, #44536538, … |
| maximal normal subgroup of | #44536532, #44536533, #44536538, … |
| maximal quotient of | #44536476, #44536478, #44536490, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 82);