Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#11745281 |
| Fitting | C2×Q16×C29 ⋊ C2 |
| Sylow | C29 ⋊ C2×#135 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #16821198, #16821203, #16821240, … |
| maximal normal subgroup of | #16821198, #16821203, #16821240, … |
| maximal quotient of | C2×#14271158, C2×#14271200, C2×#14271245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1332);