Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #478×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3228 |
370 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^2=e,c^2=e,d^2=g,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^d=h^78773 conjugacy classes — view the full character table.
| maximal subgroup of | #3228×D79, C2×#23774535, #35160359, … |
| maximal normal subgroup of | #3228×D79, C2×#23774535, #35160359, … |
| maximal quotient of | #34297763, #34297975, #34298805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 15645);