Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7422 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C47 · Schur multiplier (H2) = C2 |
| direct product | C47×#7425 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C47 | #1347 |
| commutator | C2×C16 | C2×C4×C47 |
| Frattini, cosocle | C2×M32 | C22×C47 |
| prime radical | C23×C47 | SD32 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C47 ◁ C2×C4×C47 ◁ C22×C8×C47 ◁ C2×M32×C47 ◁ G | |
136 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1457 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 413);