Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q16×D29 |
| Fitting | C2×Q16×C29 ⋊ C2 |
| Sylow | C29 ⋊ C22×Q16 |
258 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#358, #16821210, D29×#362, … |
| maximal normal subgroup of | D29×#358, #16821210, D29×#362, … |
| maximal quotient of | C2×#103×D29, C2×#107×D29, C4×Q16×D29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1324);