Finite Group DatabasebetaFinite Group Databasebeta| order | 18600 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 230400 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C5 |
| abelian | C2×C3×C4×C52×C31 |
| multiplicative | (ℤ/18971)ˣ, (ℤ/20471)ˣ, (ℤ/24025)ˣ, (ℤ/37942)ˣ, (ℤ/40942)ˣ, (ℤ/48050)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C3×C52×C31 |
| socle, prime radical | C22×C3×C52×C31 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
256 conjugacy classes of subgroups.
18600 conjugacy classes. The character table is too large to display.
| automorphism group of | C61×C311, C11×C1861 |
| outer automorphism group of | C61×C311, C11×C1861 |
Past the SmallGroups library coverage — no SmallGroups id.