Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #7316 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C29 · Schur multiplier (H2) = C23 |
| direct product | C29×#7317 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | #1304 |
| commutator | C24 | C42×C29 |
| Frattini, cosocle | C23×Q8 | C22×C29 |
| prime radical | C24×C29 | C42 |
| LCS | G ▷ C24 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C23×C29 ◁ C23×Q8×C29 ◁ G | |
432 conjugacy classes of subgroups.
812 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 305);