Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C29 ⋊ C4 |
| Sylow | C29 ⋊ #441 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=e,b^2=f,c^2=e,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 | #16835897, #16835898, #16835899, … |
| maximal normal subgroup of | #16835897, #16835898, #16835899, … |
| maximal quotient of | #16835085, #16835086, #16835087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1589);