Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | #99×D179 |
| Fitting | #99×C179 ⋊ C2 |
| Sylow | C179 ⋊ C2×#99 |
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1001 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽16)×D179, #352×D179, #37510643, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D179, #352×D179, #37510643, … |
| maximal quotient of | #323×D179, #324×D179, #37507315, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 518);