Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C29 · Schur multiplier (H2) = C22 |
| direct product | C29×#7480 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | #357 |
| commutator | C16 | C42×C29 |
| Frattini, cosocle | C22×C16 | C22×C29 |
| socle | C2×C29 | #1380 |
| prime radical | C23×C29 | SD32 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C22×C4×C29 ◁ C22×C8×C29 ◁ C22×C16×C29 ◁ G | |
166 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 468);