Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#19099293 |
| Sylow | C79 ⋊ C2×Q82 |
1112 conjugacy classes of subgroups; only the 581 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 581 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34180034, #34180385, #34180389, … |
| maximal normal subgroup of | #34180034, #34180385, #34180389, … |
| maximal quotient of | C2×#23766312, C2×#23766314, C2×#23766486, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 18085);