Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C79 ⋊ #1747 |
200 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=e,b^2=f,c^2=d,d^2=g,b^a=bd,f^a=fg,h^a=h^78,e^b=eg,h^b=h^78,h^c=h^78902 conjugacy classes — view the full character table.
| maximal subgroup of | #34198806, #34198808, #34198812, … |
| maximal normal subgroup of | #34198806, #34198808, #34198812, … |
| maximal quotient of | #34178709, #34178713, #34178717, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4266);