Finite Group DatabasebetaFinite Group Databasebeta| order | 18864 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 149760 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C9×C131 |
| multiplicative | (ℤ/24985)ˣ, (ℤ/29193)ˣ, (ℤ/35505)ˣ, (ℤ/38924)ˣ, (ℤ/49970)ˣ, (ℤ/58386)ˣ, (ℤ/71010)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C3×C131 |
| socle, prime radical | C23×C3×C131 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
162 conjugacy classes of subgroups.
18864 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.