Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ #461 |
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=f,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^28,e^c=ef215 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#461, C2×#14271366, #16828943, … |
| maximal normal subgroup of | D29×#461, C2×#14271366, #16828943, … |
| maximal quotient of | #16818865, #16818869, #16818879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 752);