Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7168 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C29×C128 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C64 | C22×C29 |
| socle | C22×C29 | C64 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
46 conjugacy classes of subgroups.
7424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C29×C256, C4×C29×C128, C22×C29×C128, … |
| maximal normal subgroup of | C2×C29×C256, C4×C29×C128, C22×C29×C128, … |
| maximal quotient of | C2×C29×C256, C4×C29×C128, C22×C29×C128, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 537);