Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43×C29 · Schur multiplier (H2) = C22×C43 |
| direct product | C29×#20329 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C29 | C24 |
| commutator | C2 | C2×C43×C29 |
| Frattini, cosocle | C22×C4 | C24×C29 |
| socle | C23×C29 | C23×C4 |
| prime radical | C24×C29 | C22×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C29 ◁ G | |
1502 conjugacy classes of subgroups; only the 1294 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 1294 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3944 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 13317);