Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q16×C29 ⋊ C2 |
| Sylow | C29 ⋊ #464 |
112 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|b^2=df,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^28,g^b=g^28,e^c=ef215 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#464, C2×#14271387, #16828943, … |
| maximal normal subgroup of | D29×#464, C2×#14271387, #16828943, … |
| maximal quotient of | #16818910, #16818924, #16818938, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 773);