Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C47 · Schur multiplier (H2) = C27 |
| direct product | C47×#10745 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C47 | #120 |
| commutator | C23 | C2×C42×C47 |
| Frattini, cosocle | C25 | C23×C47 |
| prime radical | C23×D4×C47 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C47 ◁ C25×C47 ◁ G | |
1794 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, 3733);