Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82×C29 · Schur multiplier (H2) = C23×C8 |
| direct product | C8×C29×C22⋊C8 |
| unambiguous semidirect product | C22⋊(C82×C29) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C8×C29 | C22 |
| commutator | C2 | C2×C82×C29 |
| Frattini, cosocle | C2×C42 | C23×C29 |
| socle | C23×C29 | C2×C42 |
| prime radical | C24×C29 | C42 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C8×C29 ◁ G | |
726 conjugacy classes of subgroups.
4640 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 1131);