Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1339 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C23×#1339 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #327 |
| commutator | C2×C8 | C22×C4×C23 |
| Frattini, cosocle | C2×M16 | C23×C23 |
| prime radical | C2×C23×#469 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C22×M16×C23 ◁ G | |
496 conjugacy classes of subgroups.
920 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 4671);