Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C47 · Schur multiplier (H2) = C2×C4 |
| direct product | C47×#7034 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C47 | #95 |
| commutator | C23 | C4×C8×C47 |
| Frattini, cosocle | C22×C42 | C22×C47 |
| prime radical | C24×C47 | C42 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C47 ◁ C22×C42×C47 ◁ G | |
406 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 22);