Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×Q8×C29 ⋊ C2 |
| Sylow | C29 ⋊ #460 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^28,e^c=ef299 conjugacy classes — view the full character table.
| maximal subgroup of | #16818551, #16818553, #16818557, … |
| maximal normal subgroup of | #16818551, #16818553, #16818557, … |
| maximal quotient of | #16818840, #16818852, #16818862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 749);