Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13360 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C29 · Schur multiplier (H2) = C24 |
| direct product | C29×#13361 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | #2021 |
| commutator, Frattini, cosocle | C2×#41 | C23×C29 |
| prime radical | C29×#3021 | C2 |
| LCS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C2×#41×C29 ◁ G | |
686 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 94 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, 6349);