Finite Group DatabasebetaFinite Group Databasebeta| order | 14752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C461 ⋊ C2 |
| Sylow | C461 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3688 |
Polycyclic presentation:
2^5,461|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^460,d^b=de,f^b=f^4602311 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44442245, #44442246, #44442250, … |
| maximal normal subgroup of | #44442245, #44442246, #44442250, … |
| maximal quotient of | #44442078, #44442082, #44442118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14752, 174);