Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×(C2×D79)⋊C8 |
| Fitting | C2×C4×C8×C79 ⋊ C2 |
| Sylow | C79 ⋊ C4×C22⋊C8 |
436 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 181 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 | #34178733, C8×(C2×D79)⋊C8, #34178737, … |
| maximal normal subgroup of | #34178733, C8×(C2×D79)⋊C8, #34178737, … |
| maximal quotient of | C8×(C2×D79)⋊C8, #34178739, #34178748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4269);