Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #464×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3250 |
360 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|d^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,h^b=h^78,f^c=fg,h^c=h^78773 conjugacy classes — view the full character table.
| maximal subgroup of | #3250×D79, C2×#23774750, #35161099, … |
| maximal normal subgroup of | #3250×D79, C2×#23774750, #35161099, … |
| maximal quotient of | #34298162, #34298163, #34298642, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 15860);