Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#13045 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C23 |
| Frattini, cosocle | C2×#41 | C23×C23 |
| socle | C2×C23 | #1889 |
| prime radical | C23×#3025 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C2×C4×C23 ◁ C2×#41×C23 ◁ G | |
654 conjugacy classes of subgroups.
920 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 6033);