Finite Group DatabasebetaFinite Group Databasebeta| order | 18240 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6193152 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C5×C8×C19 |
| multiplicative | (ℤ/40216)ˣ, (ℤ/42616)ˣ, (ℤ/42784)ˣ, (ℤ/54744)ˣ, (ℤ/54792)ˣ, (ℤ/54816)ˣ, (ℤ/55008)ˣ, (ℤ/60324)ˣ, (ℤ/63924)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C24×C3×C5×C19 |
| socle, prime radical | C24×C3×C5×C19 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1352 conjugacy classes of subgroups.
18240 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.