Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C29×#97 ⋊ C2 |
| Sylow | C29 ⋊ #433 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=e,c^2=d,e^2=f,b^a=bd,g^a=g^28,c^b=cf,g^b=g^28308 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#433, C2×#14271225, #16828126, … |
| maximal normal subgroup of | D29×#433, C2×#14271225, #16828126, … |
| maximal quotient of | #16819245, #16819261, #16819352, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 611);