Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#11745256 |
| Fitting | C2×C4⋊C4×C29 ⋊ C2 |
| Sylow | C29 ⋊ C2×#123 |
342 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 928 |
308 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16817839, #16822013, C4×#11745256, … |
| maximal normal subgroup of | #16817839, #16822013, C4×#11745256, … |
| maximal quotient of | C2×#14271025, C2×#14271034, C2×#14271041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1054);