Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C8×#11929608 |
| Sylow | C79 ⋊ C8×M16 |
224 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 224 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.
2576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34175159, #34175160, #34175165, … |
| maximal normal subgroup of | #34175159, #34175160, #34175165, … |
| maximal quotient of | C8×#14579072, #34177651, #34178695, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2790);