Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #343×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1908 |
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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,b^2=dfg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^78,d^b=dg,e^b=eg,f^b=fg,d^c=dg,e^c=eg,f^c=fg,h^c=h^78890 conjugacy classes — view the full character table.
| maximal subgroup of | #1908×D79, C2×#23763916, #34290204, … |
| maximal normal subgroup of | #1908×D79, C2×#23763916, #34290204, … |
| maximal quotient of | #34183744, #34183758, #34184107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5026);