Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C47 · Schur multiplier (H2) = C23 |
| direct product | C47×#12941 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C47 | #447 |
| commutator | C2×C8 | C22×C4×C47 |
| Frattini, cosocle | C22×C8 | C23×C47 |
| prime radical | C23×C47 | AGL(1,ℤ/8) |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C22×C4×C47 ◁ C47×#405 ◁ G | |
388 conjugacy classes of subgroups.
2162 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 5929);