Finite Group DatabasebetaFinite Group Databasebeta| order | 18480 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 9676800 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C24×C3×C5×C7×C11 |
| multiplicative | (ℤ/32637)ˣ, (ℤ/34293)ˣ, (ℤ/37191)ˣ, (ℤ/38056)ˣ, (ℤ/38824)ˣ, (ℤ/40744)ˣ, (ℤ/41624)ˣ, (ℤ/43516)ˣ, (ℤ/45724)ˣ, (ℤ/47432)ˣ, (ℤ/49588)ˣ, (ℤ/55464)ˣ, (ℤ/57084)ˣ, (ℤ/58236)ˣ, (ℤ/58788)ˣ, (ℤ/61116)ˣ, (ℤ/62436)ˣ, (ℤ/65274)ˣ, (ℤ/68586)ˣ, (ℤ/71148)ˣ, (ℤ/74382)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1072 conjugacy classes of subgroups.
18480 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.