Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#11745224 |
| Fitting | C2×D4×C29 ⋊ C4 |
| Sylow | C29 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 170 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 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11745224, #16835255, #16835267, … |
| maximal normal subgroup of | C4×#11745224, #16835255, #16835267, … |
| maximal quotient of | C2×D4⋊#6599, C2×#14272013, #16834784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1543);