Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C29×C4⋊C8 ⋊ C2 |
| Sylow | C29 ⋊ #431 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=e,c^2=d,e^2=f,b^a=bd,g^b=g^28,g^c=g^28320 conjugacy classes — view the full character table.
| maximal subgroup of | #16817871, #16817873, #16817881, … |
| maximal normal subgroup of | #16817871, #16817873, #16817881, … |
| maximal quotient of | #16819236, #16819249, C4⋊C8×Dic29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 601);