Finite Group DatabasebetaFinite Group Databasebeta| order | 19440 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 483729408 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C32×C9 |
| abelian | C22×C3×C4×C5×C92 |
| multiplicative | (ℤ/21793)ˣ, (ℤ/24073)ˣ, (ℤ/30951)ˣ, (ℤ/30969)ˣ, (ℤ/31293)ˣ, (ℤ/34209)ˣ, (ℤ/43586)ˣ, (ℤ/48146)ˣ, (ℤ/61902)ˣ, (ℤ/61938)ˣ, (ℤ/62586)ˣ, (ℤ/68418)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C32 | C23×C33×C5 |
| socle, prime radical | C23×C33×C5 | C2×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6804 conjugacy classes of subgroups.
19440 conjugacy classes. The character table is too large to display.
| automorphism group of | C19×C31×C37, C27×C31×C37, C19×C27×C61 |
| outer automorphism group of | C19×C31×C37, C27×C31×C37, C19×C27×C61 |
Past the SmallGroups library coverage — no SmallGroups id.