Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ #423 |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=e,b^2=d,e^2=f,b^a=bd,c^a=cf,g^b=g^28308 conjugacy classes — view the full character table.
| maximal subgroup of | #16817442, #16819482, #16819483, … |
| maximal normal subgroup of | #16817442, #16819482, #16819483, … |
| maximal quotient of | #16818247, #16818250, #16818253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 572);