Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#19098388 |
| Sylow | C79 ⋊ C2×#366 |
168 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34203667, C4×#19098388, #34203675, … |
| maximal normal subgroup of | #34203667, C4×#19098388, #34203675, … |
| maximal quotient of | C2×#23761471, #34199910, #34199949, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6286);