Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C29 ⋊ #381 |
218 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=f,c^2=d,b^a=bd,c^a=ce,g^c=g^28308 conjugacy classes — view the full character table.
| maximal subgroup of | #16817421, #16819408, #16819568, … |
| maximal normal subgroup of | #16817421, #16819408, #16819568, … |
| maximal quotient of | #16817714, #16817716, #16817739, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 410);