Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C47 · Schur multiplier (H2) = C24 |
| direct product | C47×#13305 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C47 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C47 |
| prime radical | C2×C47×#466 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C47 ◁ C23×C4×C47 ◁ C23×C8×C47 ◁ G | |
618 conjugacy classes of subgroups.
2444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 6293);