Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C29 ⋊ #407 |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^28476 conjugacy classes — view the full character table.
| maximal subgroup of | #16817344, #16817345, #16817368, … |
| maximal normal subgroup of | #16817344, #16817345, #16817368, … |
| maximal quotient of | #16817819, #16817822, #16817826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 513);