Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 28672 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C4×C29×C64 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C2×C32 | C22×C29 |
| socle | C22×C29 | C2×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
86 conjugacy classes of subgroups.
7424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C29×C128, C8×C29×C64, C2×C4×C29×C64, … |
| maximal normal subgroup of | C4×C29×C128, C8×C29×C64, C2×C4×C29×C64, … |
| maximal quotient of | C4×C29×C128, C8×C29×C64, C2×C4×C29×C64, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 497);