Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#11745182 |
| Sylow | C29 ⋊ C2×#99 |
210 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 464 |
302 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16817610, #16817611, #16817616, … |
| maximal normal subgroup of | #16817610, #16817611, #16817616, … |
| maximal quotient of | C2×#14270887, C2×#14270889, #16817810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 520);