Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C29×#97 ⋊ C2 |
| Sylow | C29 ⋊ #440 |
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^28,d^b=df,g^b=g^28302 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#440, C2×#14271265, #16828287, … |
| maximal normal subgroup of | D29×#440, C2×#14271265, #16828287, … |
| maximal quotient of | #16818306, #16818351, #16818372, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 651);