Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #441×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2943 |
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|a^2=f,c^2=f,d^2=g,e^2=g,b^a=be,c^a=cg,e^a=eg,e^b=eg,h^b=h^78,h^d=h^78902 conjugacy classes — view the full character table.
| maximal subgroup of | #34441714, #2943×D79, C2×#23772199, … |
| maximal normal subgroup of | #34441714, #2943×D79, C2×#23772199, … |
| maximal quotient of | #34257674, #34257840, #34258045, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13309);