Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q16×#1181 |
| Fitting | Q16×C29 ⋊ C4 |
| Sylow | C29 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
77 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×#1181, Q32×#1181, #16835888, … |
| maximal normal subgroup of | SD32×#1181, Q32×#1181, #16835888, … |
| maximal quotient of | Q16×#6599, #16835079, #16835080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1587);