Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C29 ⋊ #364 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=d,b^2=c,c^2=f,d^2=e,e^2=f,b^a=bc,c^a=cf,g^b=g^28308 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#364, C2×#14270983, #16821256, … |
| maximal normal subgroup of | D29×#364, C2×#14270983, #16821256, … |
| maximal quotient of | #16817555, #16817561, #16817573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 369);