Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C29 ⋊ #413 |
150 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 48 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,e^2=f,b^a=bd,d^a=df,g^a=g^12,e^b=ef,g^e=g^28134 conjugacy classes — view the full character table.
| maximal subgroup of | #16834583, #16834584, #16834592, … |
| maximal normal subgroup of | #16834583, #16834584, #16834592, … |
| maximal quotient of | #16834723, #16834725, #16834727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1535);