Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C47 · Schur multiplier (H2) = C22 |
| direct product | C47×#7417 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C47 | AΣL(1,𝔽16) |
| commutator | C2×C4⋊C4 | C2×C4×C47 |
| Frattini, cosocle | #384 | C22×C47 |
| prime radical | C47×#537 | C4 |
| LCS | G ▷ C2×C4⋊C4 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C23×C47 ◁ C22×C4×C47 ◁ C47×#384 ◁ G | |
228 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 228 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, 405);