Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C29×#101 ⋊ C2 |
| Sylow | C29 ⋊ #471 |
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|b^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^28,g^b=g^28,e^c=ef,g^c=g^28170 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#471, C2×#14271429, #16829211, … |
| maximal normal subgroup of | D29×#471, C2×#14271429, #16829211, … |
| maximal quotient of | #16818836, #16818843, #16818866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 815);