Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C29×C4⋊C8 ⋊ C2 |
| Sylow | C29 ⋊ #432 |
110 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,c^a=cf,g^b=g^28,g^c=g^28308 conjugacy classes — view the full character table.
| maximal subgroup of | #16817923, #16817925, #16817933, … |
| maximal normal subgroup of | #16817923, #16817925, #16817933, … |
| maximal quotient of | #16819239, #16819253, #16819347, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 605);