Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C23 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C23×#2140 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C2×D8 |
| commutator | C8 | C23×C4×C23 |
| Frattini, cosocle | C2×C8 | C24×C23 |
| prime radical | C23×D8×C23 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C23×C4×C23 ◁ C23×C8×C23 ◁ G | |
1406 conjugacy classes of subgroups.
1472 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 26365);