Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #3244 |
320 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^2=eg,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^78,f^c=fg,h^c=h^78767 conjugacy classes — view the full character table.
| maximal subgroup of | #3244×D79, C2×#23774696, #35160514, … |
| maximal normal subgroup of | #3244×D79, C2×#23774696, #35160514, … |
| maximal quotient of | #34297826, #34298041, #34298853, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 15806);