Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×C79⋊#564 |
| unambiguous semidirect product | (C2×C79)⋊#564 |
| Sylow | C79 ⋊ C2×#564 |
896 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 469 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 | #34180723, #34180724, C2×#23762701, … |
| maximal normal subgroup of | #34180723, #34180724, C2×#23762701, … |
| maximal quotient of | C2×#23766582, C2×#23766583, C2×#23766584, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 18653);