Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | #343×D79 |
| Fitting | #343×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#343 |
432 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
902 conjugacy classes — view the full character table.
| maximal subgroup of | #1345×D79, #1346×D79, #34198473, … |
| maximal normal subgroup of | #1345×D79, #1346×D79, #34198473, … |
| maximal quotient of | #1280×D79, #34177864, #34177867, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4244);