Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #2070 |
196 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=de,b^2=d,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^78,c^b=cf,f^b=fg,h^b=h^78,d^c=dg,h^c=h^78881 conjugacy classes — view the full character table.
| maximal subgroup of | #2070×D79, C2×#23764802, #34316992, … |
| maximal normal subgroup of | #2070×D79, C2×#23764802, #34316992, … |
| maximal quotient of | #34192906, #34192920, #34192934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5912);