Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33348 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C29 · Schur multiplier (H2) = C26 |
| direct product | C29×#33348 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | C22×#99 |
| commutator | C23 | C23×C4×C29 |
| Frattini, cosocle | C2×D4 | C24×C29 |
| prime radical | C29×#3484 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×D4×C29 ◁ C2×C29×H(5,𝔽2) ◁ G | |
1410 conjugacy classes of subgroups.
1334 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 26336);