Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #31077 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C22×C4 |
| direct product | C23×#32703 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | H(3,𝔽4) |
| commutator, Frattini, cosocle | C22×C4 | C24×C23 |
| socle | C2×C23 | #2782 |
| prime radical | C23×#575 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C22×C4×C23 ◁ G | |
476 conjugacy classes of subgroups.
782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 25691);