Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×D29⋊M16 |
| unambiguous semidirect product | D29⋊(C2×M16) |
| Sylow | C29 ⋊ C22×M16 |
298 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 464 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | #16835154, #16835157, C2×#14272030, … |
| maximal normal subgroup of | #16835154, #16835157, C2×#14272030, … |
| maximal quotient of | C2×#14272122, C2×C4×#90800, C4×D29⋊M16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1622);