Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C29×#124 ⋊ C2 |
| Sylow | C29 ⋊ #496 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^28,c^b=cf,g^b=g^28212 conjugacy classes — view the full character table.
| maximal subgroup of | #16817648, #16817650, #16818781, … |
| maximal normal subgroup of | #16817648, #16817650, #16818781, … |
| maximal quotient of | #16819116, #16819122, #16819133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 939);