Finite Group DatabasebetaFinite Group Databasebeta| order | 21600 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 79626240 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4×C5 |
| abelian | C2×C3×C42×C52×C9 |
| multiplicative | (ℤ/24827)ˣ, (ℤ/25883)ˣ, (ℤ/28055)ˣ, (ℤ/28675)ˣ, (ℤ/28975)ˣ, (ℤ/31675)ˣ, (ℤ/33123)ˣ, (ℤ/40725)ˣ, (ℤ/41175)ˣ, (ℤ/44164)ˣ, (ℤ/49654)ˣ, (ℤ/51766)ˣ, (ℤ/56110)ˣ, (ℤ/57350)ˣ, (ℤ/57950)ˣ, (ℤ/63350)ˣ, (ℤ/66246)ˣ, (ℤ/81450)ˣ, (ℤ/82350)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3 | C23×C32×C52 |
| socle, prime radical | C23×C32×C52 | C22×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4320 conjugacy classes of subgroups.
21600 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.