Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C47 · Schur multiplier (H2) = C213 |
| direct product | C2×C47×#3555 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C47 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C47 |
| prime radical | C2×#121×C47 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C47 ◁ G | |
6446 conjugacy classes of subgroups.
3572 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 55739);