Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#19099313 |
| Sylow | C79 ⋊ C2×#563 |
1024 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1024 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34180714, #34180717, #34204096, … |
| maximal normal subgroup of | #34180714, #34180717, #34204096, … |
| maximal quotient of | C2×#23766550, C2×#23766560, C2×#23766574, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 18640);