Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2121 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C29 · Schur multiplier (H2) = C23 |
| direct product | C29×#11453 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | C2×#99 |
| commutator | C23 | C22×C8×C29 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C29 |
| prime radical | C25×C29 | C2×C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C24×C29 ◁ C22×C22⋊C4×C29 ◁ G | |
562 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1334 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 4441);