Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #441×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3125 |
384 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^78,f^c=fg,h^c=h^78890 conjugacy classes — view the full character table.
| maximal subgroup of | #3125×D79, C2×#23773675, #35156639, … |
| maximal normal subgroup of | #3125×D79, C2×#23773675, #35156639, … |
| maximal quotient of | #34288377, #34291358, #34291379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14785);