Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10690 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C29 · Schur multiplier (H2) = C23 |
| direct product | C29×#10691 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | #401 |
| commutator, Frattini, cosocle | C25 | C23×C29 |
| prime radical | C25×C29 | C23 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C25×C29 ◁ G | |
372 conjugacy classes of subgroups.
725 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 3679);