Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C29 ⋊ #347 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,g^a=g^12,c^b=cf,g^b=g^28,g^c=g^28134 conjugacy classes — view the full character table.
| maximal subgroup of | #16835709, C2×#14272056, #16835714, … |
| maximal normal subgroup of | #16835709, C2×#14272056, #16835714, … |
| maximal quotient of | #16834410, #16834534, C2×#14272056 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1442);