Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C29 · Schur multiplier (H2) = C23 |
| direct product | C29×#11688 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | #327 |
| commutator | C2×C8 | C22×C4×C29 |
| Frattini, cosocle | C2×M16 | C23×C29 |
| socle | C2×C29 | C2×#327 |
| prime radical | C29×#3054 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C22×C4×C29 ◁ C22×M16×C29 ◁ G | |
432 conjugacy classes of subgroups.
1160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 4676);