Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | D8×C29 ⋊ C4 |
| Sylow | C29 ⋊ #442 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 232 |
Polycyclic presentation:
2^6,29|a^2=e,c^2=ef,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^17,d^b=df,g^c=g^12,g^e=g^2871 conjugacy classes — view the full character table.
| maximal subgroup of | #16835901, #16835902, #16835903, … |
| maximal normal subgroup of | #16835901, #16835902, #16835903, … |
| maximal quotient of | #16835088, #16835089, #16835090, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1590);