Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #1838 |
180 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=f,b^2=e,c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^78,c^b=cg1592 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34175439, #34182668, #34182669, … |
| maximal normal subgroup of | #34175439, #34182668, #34182669, … |
| maximal quotient of | #34181936, #34181940, #34181943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4651);