Finite Group DatabasebetaFinite Group Databasebeta| order | 15968 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #41×C499 ⋊ C2 |
| Sylow | C499 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3992 |
Polycyclic presentation:
2^5,499|d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^b=f^4982501 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44543266, #44543267, #44543271, … |
| maximal normal subgroup of | #44543266, #44543267, #44543271, … |
| maximal quotient of | #44543099, #44543102, #44543141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15968, 171);