Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #485×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3121 |
370 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^78,d^b=dg,f^c=fg,h^c=h^78,h^d=h^78773 conjugacy classes — view the full character table.
| maximal subgroup of | #3121×D79, C2×#23773632, #35156633, … |
| maximal normal subgroup of | #3121×D79, C2×#23773632, #35156633, … |
| maximal quotient of | #34288365, #34291378, #34291397, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14742);