Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C29 · Schur multiplier (H2) = C22 |
| direct product | C29×#12885 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C29 | #124 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C8 | C23×C29 |
| socle | C2×C29 | #1832 |
| prime radical | C23×C29 | #131 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C29 ◁ C22×C8×C29 ◁ G | |
234 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 122 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, 5873);