Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #1746 |
240 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,h^a=h^78,c^b=cg1616 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34178723, #34178728, #34179312, … |
| maximal normal subgroup of | #34178723, #34178728, #34179312, … |
| maximal quotient of | #34178696, #34178699, #34178701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4262);