Finite Group DatabasebetaFinite Group Databasebeta| order | 21600 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3317760 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C3×C42×C9×C25 |
| multiplicative | (ℤ/24947)ˣ, (ℤ/26159)ˣ, (ℤ/27935)ˣ, (ℤ/30875)ˣ, (ℤ/32375)ˣ, (ℤ/33633)ˣ, (ℤ/35451)ˣ, (ℤ/41625)ˣ, (ℤ/43875)ˣ, (ℤ/49894)ˣ, (ℤ/52318)ˣ, (ℤ/55870)ˣ, (ℤ/61750)ˣ, (ℤ/64750)ˣ, (ℤ/67266)ˣ, (ℤ/70902)ˣ, (ℤ/83250)ˣ, (ℤ/87750)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3×C5 | C23×C32×C5 |
| socle, prime radical | C23×C32×C5 | C22×C3×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1620 conjugacy classes of subgroups.
21600 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C19×C101, C13×C19×C125, C7×C37×C125 |
| outer automorphism group of | C13×C19×C101, C13×C19×C125, C7×C37×C125 |
Past the SmallGroups library coverage — no SmallGroups id.