Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ #338 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,e^a=ef,d^b=df,g^b=g^28302 conjugacy classes — view the full character table.
| maximal subgroup of | #16817483, #16817484, #16817486, … |
| maximal normal subgroup of | #16817483, #16817484, #16817486, … |
| maximal quotient of | #16817322, #16817323, #16817363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 307);