Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C47 · Schur multiplier (H2) = C27×C4 |
| direct product | C47×#60128 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C47 | C25 |
| commutator | C22 | C24×C4×C47 |
| Frattini, cosocle | C2×C4 | C25×C47 |
| socle | C22×C47 | C24×C4 |
| prime radical | C22×#41×C47 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C47 ◁ G | |
2124 conjugacy classes of subgroups.
4136 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 53116);