Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×#1181 |
| unambiguous semidirect product | D29⋊(C4×Q8) |
| Fitting | C2×Q8×C29 ⋊ C4 |
| Sylow | C29 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | #101×#1181, #103×#1181, #16835265, … |
| maximal normal subgroup of | #101×#1181, #103×#1181, #16835265, … |
| maximal quotient of | C2×C4⋊C4×#1181, C4×Q8×#1181, C2×#14272112, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1614);