Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12102 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C29 · Schur multiplier (H2) = C22 |
| direct product | C29×#12279 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C29 |
| prime radical | C24×C29 | D8 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C29×C22⋊C8 ◁ G | |
344 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 5267);