Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C29 · Schur multiplier (H2) = C26 |
| direct product | C29×#8316 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C29 | #120 |
| commutator | C23 | C22×C8×C29 |
| Frattini, cosocle | C23×C4 | C23×C29 |
| socle | C22×C29 | #379 |
| prime radical | C2×C29×H(5,𝔽2) | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C23×C4×C29 ◁ G | |
1118 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 218 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, 1304);