Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17411 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C29 · Schur multiplier (H2) = C25 |
| direct product | C29×#22539 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C29 |
| Frattini, cosocle | C22×C4 | C24×C29 |
| prime radical | C2×C29×#127 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C4×Q8×C29 ◁ G | |
1066 conjugacy classes of subgroups.
1595 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 15527);