Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #487×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3167 |
412 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^78,h^b=h^78,h^c=h^78,h^d=h^78902 conjugacy classes — view the full character table.
| maximal subgroup of | #34264231, #34264233, #34264250, … |
| maximal normal subgroup of | #34264231, #34264233, #34264250, … |
| maximal quotient of | #34288801, #34292473, #34293441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 15072);