Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C47 · Schur multiplier (H2) = C2×C4 |
| direct product | C47×#7190 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C47 | #99 |
| commutator | C2×C4 | C4×C8×C47 |
| Frattini, cosocle | C2×#117 | C22×C47 |
| socle | C22×C47 | #342 |
| prime radical | C24×C47 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C47 ◁ C22×C4×C47 ◁ C2×#117×C47 ◁ G | |
322 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 110 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, 178);