Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C47 · Schur multiplier (H2) = C28 |
| direct product | Q8×AGL(1,ℤ/8)×C47 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C47 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C47 |
| prime radical | C2×AGL(1,ℤ/8)×C47 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C2×C4×Q8×C47 ◁ G | |
2010 conjugacy classes of subgroups.
2585 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 54354);