Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C22×C4×D316 |
| Fitting | C22×C42×C79 ⋊ C2 |
| Sylow | C79 ⋊ C22×C4×D4 |
2528 conjugacy classes of subgroups; only the 981 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 981 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34179609, #34179635, #34179637, … |
| maximal normal subgroup of | #34179609, #34179635, #34179637, … |
| maximal quotient of | C22×C4×(C2×D79)⋊C4, C22×C4×C4⋊Dic79, C2×C42×D316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17682);