Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C29 · Schur multiplier (H2) = C43 |
| direct product | C29×#32712 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C29 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C29 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C22×#41×C29 ◁ G | |
964 conjugacy classes of subgroups.
986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 25700);