Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29×C32 · Schur multiplier (H2) = C22 |
| direct product | C29×D4⋊C32 |
| unambiguous semidirect product | D4⋊(C29×C32) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C29 | D4 |
| commutator | C4 | C2×C29×C32 |
| Frattini, cosocle | C4×C16 | C22×C29 |
| socle | C22×C29 | C22⋊C16 |
| prime radical | C2×D4×C29 | C16 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C29 ◁ C4×C16×C29 ◁ G | |
138 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 367);