Finite Group DatabasebetaFinite Group Databasebeta| order | 21056 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 565248 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C4×C7×C8×C47 |
| multiplicative | (ℤ/39495)ˣ, (ℤ/42128)ˣ, (ℤ/52660)ˣ, (ℤ/78990)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C23×C7×C47 |
| socle, prime radical | C23×C7×C47 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
324 conjugacy classes of subgroups.
21056 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.