Finite Group DatabasebetaFinite Group Databasebeta| order | 20160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 294912 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C4×C5×C7×C8×C9 |
| multiplicative | (ℤ/22591)ˣ, (ℤ/23287)ˣ, (ℤ/25915)ˣ, (ℤ/26035)ˣ, (ℤ/26695)ˣ, (ℤ/31191)ˣ, (ℤ/32103)ˣ, (ℤ/37815)ˣ, (ℤ/37935)ˣ, (ℤ/40336)ˣ, (ℤ/41588)ˣ, (ℤ/45182)ˣ, (ℤ/46574)ˣ, (ℤ/50420)ˣ, (ℤ/51830)ˣ, (ℤ/52070)ˣ, (ℤ/53390)ˣ, (ℤ/62382)ˣ, (ℤ/64206)ˣ, (ℤ/75630)ˣ, (ℤ/75870)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C4 | C23×C3×C5×C7 |
| socle, prime radical | C23×C3×C5×C7 | C2×C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
972 conjugacy classes of subgroups.
20160 conjugacy classes. The character table is too large to display.
| automorphism group of | C19×C29×C41, C27×C29×C41 |
| outer automorphism group of | C19×C29×C41, C27×C29×C41 |
Past the SmallGroups library coverage — no SmallGroups id.