Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C22⋊C4×C29 ⋊ C4 |
| Sylow | C29 ⋊ #388 |
190 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 54 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=f,b^2=df,c^2=d,b^a=bd,c^a=ce,g^a=g^17,g^b=g^12,g^f=g^2898 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14272113, #16835946, #16835949, … |
| maximal normal subgroup of | C2×#14272113, #16835946, #16835949, … |
| maximal quotient of | #16834667, #16834672, #16834673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1499);