Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| 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^a=g^12,g^b=g^28,g^c=g^28,g^e=g^28152 conjugacy classes — view the full character table.
| maximal subgroup of | #16834319, #16834324, #16834347, … |
| maximal normal subgroup of | #16834319, #16834324, #16834347, … |
| maximal quotient of | #16835207, C4×#11745219, C4×C4⋊#6599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1568);