Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1357 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C29 · Schur multiplier (H2) = C22 |
| direct product | C29×#7268 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | #331 |
| commutator | C42 | C42×C29 |
| Frattini, cosocle | C2×C4×C8 | C22×C29 |
| prime radical | C23×C29 | #100 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C4×C8×C29 ◁ G | |
238 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1334 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 256);