Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C29 · Schur multiplier (H2) = C22 |
| direct product | C29×#7347 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | AΣL(1,𝔽16) |
| commutator | C2×Q8 | C2×C8×C29 |
| Frattini, cosocle | #408 | C22×C29 |
| socle | C2×C29 | #1316 |
| prime radical | C29×#585 | C4 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C2×C4×C29 ◁ C22×C4×C29 ◁ C29×#408 ◁ G | |
318 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 318 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.
986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 335);