Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #2072 |
238 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 238 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=e,b^2=g,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^78,c^b=cf,f^b=fg,f^c=fg1124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2072×D79, C2×#23764811, #34317026, … |
| maximal normal subgroup of | #2072×D79, C2×#23764811, #34317026, … |
| maximal quotient of | #34192982, #34192987, #34192999, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5921);