Finite Group DatabasebetaFinite Group Databasebeta| order | 21504 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 301989888 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C43 |
| abelian | C2×C3×C42×C7×C32 |
| multiplicative | (ℤ/42195)ˣ, (ℤ/45008)ˣ, (ℤ/48256)ˣ, (ℤ/53840)ˣ, (ℤ/56260)ˣ, (ℤ/84390)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C16 | C24×C3×C7 |
| socle, prime radical | C24×C3×C7 | C22×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
7188 conjugacy classes of subgroups.
21504 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.