Finite Group DatabasebetaFinite Group Databasebeta| order | 21504 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 57982058496 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C27×C43 |
| abelian | C22×C3×C42×C7×C16 |
| multiplicative | (ℤ/51272)ˣ, (ℤ/51765)ˣ, (ℤ/55216)ˣ, (ℤ/58480)ˣ, (ℤ/58760)ˣ, (ℤ/63280)ˣ, (ℤ/64960)ˣ, (ℤ/66640)ˣ, (ℤ/69020)ˣ, (ℤ/70512)ˣ, (ℤ/70992)ˣ, (ℤ/72384)ˣ, (ℤ/76908)ˣ, (ℤ/80880)ˣ, (ℤ/81360)ˣ, (ℤ/83520)ˣ, (ℤ/88140)ˣ, (ℤ/88740)ˣ, (ℤ/103530)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C8 | C25×C3×C7 |
| socle, prime radical | C25×C3×C7 | C22×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
36564 conjugacy classes of subgroups.
21504 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.