Finite Group DatabasebetaFinite Group Databasebeta| order | 19800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 9600 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C4×C9×C11×C25 |
| multiplicative | (ℤ/20099)ˣ, (ℤ/24755)ˣ, (ℤ/24875)ˣ, (ℤ/29703)ˣ, (ℤ/39604)ˣ, (ℤ/40198)ˣ, (ℤ/49510)ˣ, (ℤ/49750)ˣ, (ℤ/59406)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C5 | C22×C3×C5×C11 |
| socle, prime radical | C22×C3×C5×C11 | C2×C3×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
144 conjugacy classes of subgroups.
19800 conjugacy classes. The character table is too large to display.
| automorphism group of | C101×C199 |
| outer automorphism group of | C101×C199 |
Past the SmallGroups library coverage — no SmallGroups id.