Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#11745346 |
| Sylow | C29 ⋊ C2×#131 |
266 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 928 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | #16835249, #16835250, #16835267, … |
| maximal normal subgroup of | #16835249, #16835250, #16835267, … |
| maximal quotient of | C2×#14272127, C2×#14272128, C4×#11745346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1624);