Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C22×#14579152 |
| Sylow | C79 ⋊ C22×#125 |
1192 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1192 conjugacy classes of subgroups — too many to draw. Only its 645 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1616 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34180913, #34197183, #34197190, … |
| maximal normal subgroup of | #34180913, #34197183, #34197190, … |
| maximal quotient of | C22×#19098428, C22×#19098446, C22×#19098450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17762);