Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | #498×D79 |
| Fitting | #498×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#498 |
424 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 165 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 | #1654×D79, #1651×D79, #1653×D79, … |
| maximal normal subgroup of | #1654×D79, #1651×D79, #1653×D79, … |
| maximal quotient of | #1844×D79, #1941×D79, #1990×D79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 15006);