Finite Group DatabasebetaFinite Group Databasebeta| order | 20736 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 191102976 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C33×C4 |
| abelian | C2×C32×C4×C9×C32 |
| multiplicative | (ℤ/23959)ˣ, (ℤ/25123)ˣ, (ℤ/32301)ˣ, (ℤ/34047)ˣ, (ℤ/47918)ˣ, (ℤ/50246)ˣ, (ℤ/64602)ˣ, (ℤ/68094)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C16 | C23×C33 |
| socle, prime radical | C23×C33 | C2×C3×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6750 conjugacy classes of subgroups.
20736 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C19×C97 |
| outer automorphism group of | C13×C19×C97 |
Past the SmallGroups library coverage — no SmallGroups id.