Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C29 · Schur multiplier (H2) = C2 |
| direct product | C29×#7461 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C29 | D16 |
| commutator | C16 | C2×C8×C29 |
| Frattini, cosocle | C4×C16 | C22×C29 |
| socle, prime radical | C22×C29 | #366 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C42×C29 ◁ C4×C8×C29 ◁ C4×C16×C29 ◁ G | |
86 conjugacy classes of subgroups.
2204 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 449);