Finite Group DatabasebetaFinite Group Databasebeta| order | 6000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 768000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C5 |
| abelian | C22×C3×C4×C5×C25 |
| multiplicative | (ℤ/7777)ˣ, (ℤ/8305)ˣ, (ℤ/9393)ˣ, (ℤ/9625)ˣ, (ℤ/9999)ˣ, (ℤ/11325)ˣ, (ℤ/11625)ˣ, (ℤ/12375)ˣ, (ℤ/12524)ˣ, (ℤ/15100)ˣ, (ℤ/15500)ˣ, (ℤ/15554)ˣ, (ℤ/16610)ˣ, (ℤ/18786)ˣ, (ℤ/19250)ˣ, (ℤ/19998)ˣ, (ℤ/22650)ˣ, (ℤ/23250)ˣ, (ℤ/24750)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C5 | C23×C3×C52 |
| socle, prime radical | C23×C3×C52 | C2×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
756 conjugacy classes of subgroups.
6000 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.