Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #461×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3039 |
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|a^2=g,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,f^c=fg,h^d=h^78773 conjugacy classes — view the full character table.
| maximal subgroup of | #34264392, #34264396, #34264497, … |
| maximal normal subgroup of | #34264392, #34264396, #34264497, … |
| maximal quotient of | #34272184, #34272193, #34272200, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13992);