Finite Group DatabasebetaFinite Group Databasebeta| order | 24696 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 592704 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C7 |
| abelian | C2×C4×C7×C9×C49 |
| multiplicative | (ℤ/25019)ˣ, (ℤ/25607)ˣ, (ℤ/50038)ˣ, (ℤ/51214)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C7 | C22×C3×C72 |
| socle, prime radical | C22×C3×C72 | C2×C3×C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
432 conjugacy classes of subgroups.
24696 conjugacy classes. The character table is too large to display.
| automorphism group of | C127×C197, C29×C883 |
| outer automorphism group of | C127×C197, C29×C883 |
Past the SmallGroups library coverage — no SmallGroups id.