Finite Group DatabasebetaFinite Group Databasebeta| order | 21000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 9600 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C4×C7×C125 |
| multiplicative | (ℤ/21779)ˣ, (ℤ/26875)ˣ, (ℤ/30625)ˣ, (ℤ/31503)ˣ, (ℤ/42004)ˣ, (ℤ/43558)ˣ, (ℤ/53750)ˣ, (ℤ/61250)ˣ, (ℤ/63006)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C25 | C22×C3×C5×C7 |
| socle, prime radical | C22×C3×C5×C7 | C2×C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
128 conjugacy classes of subgroups.
21000 conjugacy classes. The character table is too large to display.
| automorphism group of | C29×C751, C49×C625 |
| outer automorphism group of | C29×C751, C49×C625 |
Past the SmallGroups library coverage — no SmallGroups id.