Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7035 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C29 · Schur multiplier (H2) = C23 |
| direct product | C29×#7050 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C29 | #95 |
| commutator | C22×C4 | C42×C29 |
| Frattini, cosocle | C43 | C22×C29 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C43×C29 ◁ G | |
332 conjugacy classes of subgroups.
1508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 38);