Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#19098824 |
| Sylow | C79 ⋊ C2×#471 |
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
890 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#19098824, #34295139, #34295189, … |
| maximal normal subgroup of | C4×#19098824, #34295139, #34295189, … |
| maximal quotient of | C2×#23762739, C2×#23762777, C2×#23762835, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14207);