Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C22×C4 |
| direct product | C23×#13560 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | AΣL(1,𝔽16) |
| commutator | C2×D4 | C22×C4×C23 |
| Frattini, cosocle | #127 | C23×C23 |
| socle | C2×C23 | C2×AΣL(1,𝔽16) |
| prime radical | C23×#3018 | C2 |
| LCS | G ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C2×C4×C23 ◁ C22×C4×C23 ◁ C23×#532 ◁ G | |
486 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 6548);