Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#11745225 |
| unambiguous semidirect product | D29⋊#103 |
| Fitting | C2×Q8×C29 ⋊ C4 |
| Sylow | C29 ⋊ 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.
| transitive degree | μt(G) = 464 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11745225, #103×#1181, #16835264, … |
| maximal normal subgroup of | C4×#11745225, #103×#1181, #16835264, … |
| maximal quotient of | C2×Q8⋊#6599, D29⋊(Q8⋊C8), C2×#14272013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1538);