Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#19098869 |
| Sylow | C79 ⋊ C2×#479 |
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19098869, #34295897, #34295962, … |
| maximal normal subgroup of | C4×#19098869, #34295897, #34295962, … |
| maximal quotient of | C2×#23763414, C2×#23763651, C2×#23763669, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14286);