Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#11745278 |
| Fitting | C2×SD16×C29 ⋊ C2 |
| Sylow | C29 ⋊ C2×#135 |
266 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 928 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11745278, #16828287, #16828364, … |
| maximal normal subgroup of | C4×#11745278, #16828287, #16828364, … |
| maximal quotient of | C2×#14271156, C2×#14271158, C2×#14271198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1330);