Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C491 ⋊ C2 |
| Sylow | C491 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3928 |
Polycyclic presentation:
2^5,491|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^490,d^b=de2461 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536891, #44536892, #44536896, … |
| maximal normal subgroup of | #44536891, #44536892, #44536896, … |
| maximal quotient of | #44536724, #44536730, #44536765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 172);