Finite Group DatabasebetaFinite Group Databasebeta| order | 30888 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 103680 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C3×C4×C9×C11×C13 |
| multiplicative | (ℤ/31243)ˣ, (ℤ/31363)ˣ, (ℤ/31783)ˣ, (ℤ/33631)ˣ, (ℤ/62486)ˣ, (ℤ/62726)ˣ, (ℤ/63566)ˣ, (ℤ/67262)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C22×C32×C11×C13 |
| socle, prime radical | C22×C32×C11×C13 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
320 conjugacy classes of subgroups.
30888 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.