Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C29×#117 ⋊ C2 |
| Sylow | C29 ⋊ #410 |
158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=e,c^2=f,b^a=bd,d^a=df,e^b=ef,g^b=g^28302 conjugacy classes — view the full character table.
| maximal subgroup of | #16819291, #16819293, #16819454, … |
| maximal normal subgroup of | #16819291, #16819293, #16819454, … |
| maximal quotient of | #16817804, #16817812, #16817815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 522);