Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C29 · Schur multiplier (H2) = C23 |
| direct product | C29×#32699 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | #2749 |
| commutator, Frattini, cosocle | C22×C4 | C24×C29 |
| prime radical | C2×C29×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C22×C4×C29 ◁ G | |
538 conjugacy classes of subgroups.
986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 25687);