Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#19098515 |
| Fitting | C2×#97×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×C4×M16 |
656 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 341 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34177686, #34177692, #34177898, … |
| maximal normal subgroup of | #34177686, #34177692, #34177898, … |
| maximal quotient of | C2×#23761679, C2×#23761688, C2×#23761696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 12918);