Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60750 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C29 · Schur multiplier (H2) = C27×C4 |
| direct product | C29×#60800 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C29 |
| prime radical | C29×#3444 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C42×C29 ◁ G | |
2134 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, 53788);