Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C23 · Schur multiplier (H2) = C2×C8 |
| direct product | C23×#8268 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C23 | C2×D4 |
| commutator | C4 | C2×C4×C8×C23 |
| Frattini, cosocle | C2×C42 | C23×C23 |
| socle | C22×C23 | C4×C4⋊C4 |
| prime radical | C23×C23 | #117 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C23 ◁ C2×C4×C8×C23 ◁ G | |
390 conjugacy classes of subgroups.
2024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 1256);