Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #14715 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C47 · Schur multiplier (H2) = C25 |
| direct product | C47×C22⋊#401 |
| unambiguous semidirect product | C22⋊(C47×#401) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C47 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C47 |
| prime radical | C25×C47 | C23 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C47 ◁ G | |
1650 conjugacy classes of subgroups.
3008 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 7815);