Finite Group DatabasebetaFinite Group Databasebeta| order | 6000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 38400 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C125 |
| multiplicative | (ℤ/8785)ˣ, (ℤ/9789)ˣ, (ℤ/11265)ˣ, (ℤ/11295)ˣ, (ℤ/12016)ˣ, (ℤ/13052)ˣ, (ℤ/13125)ˣ, (ℤ/15020)ˣ, (ℤ/17500)ˣ, (ℤ/17570)ˣ, (ℤ/19578)ˣ, (ℤ/22500)ˣ, (ℤ/22530)ˣ, (ℤ/22590)ˣ, (ℤ/26250)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C25 | C23×C3×C5 |
| socle, prime radical | C23×C3×C5 | C2×C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
216 conjugacy classes of subgroups.
6000 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.