Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7402 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C29 · Schur multiplier (H2) = C23 |
| direct product | C29×#7402 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | #353 |
| commutator | C2×C42 | C2×C4×C29 |
| Frattini, cosocle | #390 | C22×C29 |
| prime radical | C29×#2011 | C2 |
| LCS | G ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C29 ◁ C22×C4×C29 ◁ C29×#390 ◁ G | |
334 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
812 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 390);