Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C47 · Schur multiplier (H2) = C27 |
| direct product | C22×C47×#344 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C47 | C22⋊C4 |
| commutator | C22 | C22×C42×C47 |
| Frattini, cosocle | C22×C4 | C24×C47 |
| socle | C23×C47 | #95 |
| prime radical | C25×C47 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C47 ◁ C24×C4×C47 ◁ G | |
2190 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, 13347);