Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | #99×D277 |
| Fitting | #99×C277 ⋊ C2 |
| Sylow | C277 ⋊ 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) = 2216 |
1540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AΣL(1,𝔽16)×D277, #352×D277, #47984810, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D277, #352×D277, #47984810, … |
| maximal quotient of | #323×D277, #324×D277, #47981482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 518);