Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of AΣL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C29 · Schur multiplier (H2) = C2 |
| direct product | C29×#7365 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C29 | #99 |
| commutator | C23 | C2×C16×C29 |
| Frattini, cosocle | C2×M32 | C22×C29 |
| socle | C2×C29 | #1322 |
| prime radical | C23×C29 | C2×C16 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C29 ◁ C2×C8×C29 ◁ C2×C29×M32 ◁ G | |
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 353);