Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #488×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3168 |
380 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^78,h^c=h^78,h^d=h^78902 conjugacy classes — view the full character table.
| maximal subgroup of | #3168×D79, C2×#23773969, #35158017, … |
| maximal normal subgroup of | #3168×D79, C2×#23773969, #35158017, … |
| maximal quotient of | #34288815, #34292473, #34292477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 15079);