Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C23 · Schur multiplier (H2) = C28 |
| direct product | Q8×C23×AGL(1,ℤ/8) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C23 |
| prime radical | C2×C23×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C2×C4×Q8×C23 ◁ G | |
2010 conjugacy classes of subgroups.
1265 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 54354);