Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C29 · Schur multiplier (H2) = C4 |
| direct product | C29×#7356 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | #353 |
| commutator | C42 | C2×C8×C29 |
| Frattini, cosocle | #423 | C22×C29 |
| socle | C2×C29 | #1318 |
| prime radical | C29×#532 | C4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C2×C4×C29 ◁ C22×C4×C29 ◁ C29×#423 ◁ G | |
202 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 202 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, 344);