Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C29 ⋊ #389 |
170 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^6,29|a^2=f,b^2=f,c^2=e,b^a=bd,c^a=ce,g^c=g^28308 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#389, C2×#14271058, #16821951, … |
| maximal normal subgroup of | D29×#389, C2×#14271058, #16821951, … |
| maximal quotient of | #16817720, #16817724, #16817727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 444);