Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ #343 |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=d,b^2=e,d^2=f,b^a=bc,c^a=cf,g^a=g^28,d^b=df302 conjugacy classes — view the full character table.
| maximal subgroup of | #16817495, #16817496, #16817498, … |
| maximal normal subgroup of | #16817495, #16817496, #16817498, … |
| maximal quotient of | #16817335, #16817342, #16817348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 318);