Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M16×C29 ⋊ C2 |
| Sylow | C29 ⋊ #575 |
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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|d^2=f,e^2=f,b^a=be,c^a=cf,e^a=ef,g^a=g^28,e^b=ef,g^b=g^28302 conjugacy classes — view the full character table.
| maximal subgroup of | #16819853, #16819855, #16819992, … |
| maximal normal subgroup of | #16819853, #16819855, #16819992, … |
| maximal quotient of | #16828012, #16828082, #16828294, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1349);