Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of #7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C47 · Schur multiplier (H2) = C8 |
| direct product | C47×#7533 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C47 | #1409 |
| commutator | C4×C8 | C2×C4×C47 |
| Frattini, cosocle | #493 | C22×C47 |
| prime radical | C47×#493 | C22 |
| LCS | G ▷ C4×C8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C47 ◁ C22×C47 ◁ C2×C4×C47 ◁ C42×C47 ◁ C47×#493 ◁ G | |
156 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
893 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 521);