Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ #441 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^6,29|a^2=e,b^2=f,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,d^b=df,g^c=g^28218 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#441, C2×#14271267, #16828287, … |
| maximal normal subgroup of | D29×#441, C2×#14271267, #16828287, … |
| maximal quotient of | #16818308, #16818360, #16818366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 653);