Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C82×C29 · Schur multiplier (H2) = C2×C4 |
| direct product | C29×#7139 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C29 | C22⋊C4 |
| commutator | C22 | C82×C29 |
| Frattini, cosocle | C2×C4×C8 | C22×C29 |
| socle | C22×C29 | #336 |
| prime radical | C23×C29 | C4×C8 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C29 ◁ C2×C4×C8×C29 ◁ G | |
262 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2552 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 127);