Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C29 ⋊ #359 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=d,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^12,c^b=ce,e^b=ef,g^b=g^28,g^d=g^2871 conjugacy classes — view the full character table.
| maximal subgroup of | D29⋊#359, C2×#14272078, #16835806, … |
| maximal normal subgroup of | D29⋊#359, C2×#14272078, #16835806, … |
| maximal quotient of | #16834447, #16834448, #16834483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1464);