Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#19098921 |
| Sylow | C79 ⋊ C2×#489 |
436 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19098921, #34296334, #34296378, … |
| maximal normal subgroup of | C4×#19098921, #34296334, #34296378, … |
| maximal quotient of | C2×#23763532, C2×#23764088, C2×#23764091, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14837);