Finite Group DatabasebetaFinite Group Databasebeta| order | 11072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#19149742 |
| unambiguous semidirect product | D173⋊#103 |
| Fitting | C2×Q8×C173 ⋊ C4 |
| Sylow | C173 ⋊ C2×#103 |
162 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
458 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#19149742, #103×#10621924, #36369335, … |
| maximal normal subgroup of | C4×#19149742, #103×#10621924, #36369335, … |
| maximal quotient of | C2×Q8⋊#13063443, D173⋊(Q8⋊C8), C2×#26012341, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11072, 1538);