Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | Q8×#11929608 |
| Sylow | C79 ⋊ Q8×M16 |
388 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 241 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1610 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34182602, #34182606, #34182616, … |
| maximal normal subgroup of | #34182602, #34182606, #34182616, … |
| maximal quotient of | C4⋊C4×#11929608, #34286921, Q8×#14579072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13464);