Finite Group DatabasebetaFinite Group Databasebeta| order | 14528 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | #99×D227 |
| Fitting | #99×C227 ⋊ C2 |
| Sylow | C227 ⋊ 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.
| transitive degree | μt(G) = 1816 |
1265 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AΣL(1,𝔽16)×D227, #352×D227, #44401377, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D227, #352×D227, #44401377, … |
| maximal quotient of | #323×D227, #324×D227, #44398049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14528, 518);