Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#19098430 |
| Sylow | C79 ⋊ C2×#383 |
624 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1616 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34177891, #34178279, #34178307, … |
| maximal normal subgroup of | #34177891, #34178279, #34178307, … |
| maximal quotient of | C2×#23761624, C2×#23761625, C2×#23761626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6899);