Finite Group DatabasebetaFinite Group Databasebeta| order | 20736 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 127401984 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C8×C9 |
| abelian | C2×C8×C92×C16 |
| multiplicative | (ℤ/23579)ˣ, (ℤ/33507)ˣ, (ℤ/47158)ˣ, (ℤ/67014)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C32×C4×C8 | C23×C32 |
| socle, prime radical | C23×C32 | C32×C4×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4577 conjugacy classes of subgroups.
20736 conjugacy classes. The character table is too large to display.
| automorphism group of | C17×C19×C73 |
| outer automorphism group of | C17×C19×C73 |
Past the SmallGroups library coverage — no SmallGroups id.