Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C47 · Schur multiplier (H2) = C22 |
| direct product | C47×#7473 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C47 | D16 |
| commutator | C16 | C42×C47 |
| Frattini, cosocle | C22×C16 | C22×C47 |
| socle | C22×C47 | #357 |
| prime radical | C23×C47 | SD32 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C47 ◁ C22×C4×C47 ◁ C22×C8×C47 ◁ C22×C16×C47 ◁ G | |
170 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3572 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 461);