Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #410×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1796 |
536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,b^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,h^b=h^78,f^c=fg887 conjugacy classes — view the full character table.
| maximal subgroup of | #34203818, #34203820, #34203828, … |
| maximal normal subgroup of | #34203818, #34203820, #34203828, … |
| maximal quotient of | #34179690, #34179696, #34179701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4483);