Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×M16×C29 ⋊ C2 |
| Sylow | C29 ⋊ #436 |
122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 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|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,c^b=cf,g^b=g^28308 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#436, C2×#14271239, #16828192, … |
| maximal normal subgroup of | D29×#436, C2×#14271239, #16828192, … |
| maximal quotient of | #16818375, #16818380, #16818382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 625);