Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #329×D79 |
| Fitting | #329×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#329 |
284 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
779 conjugacy classes — view the full character table.
| maximal subgroup of | #1403×D79, #1404×D79, C2×#329×D79, … |
| maximal normal subgroup of | #1403×D79, #1404×D79, C2×#329×D79, … |
| maximal quotient of | #1270×D79, #1272×D79, #34176235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 3089);