Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C29 · Schur multiplier (H2) = C24×C4 |
| direct product | C29×#10936 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C29 | #120 |
| commutator | C23 | C2×C42×C29 |
| Frattini, cosocle | C25 | C23×C29 |
| prime radical | C25×C29 | C23 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C25×C29 ◁ G | |
1258 conjugacy classes of subgroups; only the 302 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 302 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1856 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 3924);