Finite Group DatabasebetaFinite Group Databasebeta| order | 18240 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 9216 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C5×C19×C32 |
| multiplicative | (ℤ/18527)ˣ, (ℤ/21287)ˣ, (ℤ/27369)ˣ, (ℤ/37054)ˣ, (ℤ/42574)ˣ, (ℤ/54738)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C16 | C22×C3×C5×C19 |
| socle, prime radical | C22×C3×C5×C19 | C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
136 conjugacy classes of subgroups.
18240 conjugacy classes. The character table is too large to display.
| automorphism group of | C97×C191, C7×C3041 |
| outer automorphism group of | C97×C191, C7×C3041 |
Past the SmallGroups library coverage — no SmallGroups id.