Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#11745229 |
| Sylow | C29 ⋊ C2×#100 |
186 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 464 |
134 conjugacy classes — view the full character table.
| maximal subgroup of | #16834576, #16834577, C4×#11745229, … |
| maximal normal subgroup of | #16834576, #16834577, C4×#11745229, … |
| maximal quotient of | C2×#14272006, C2×#14272007, #16834731, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1531);