Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #100×D83 |
| Fitting | #100×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#100 |
186 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 186 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.
473 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽16)×D83, #352×D83, #24909106, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D83, #352×D83, #24909106, … |
| maximal quotient of | #343×D83, #24907254, #100×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 524);