Finite Group DatabasebetaFinite Group Databasebeta| order | 21168 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 41803776 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3×C7 |
| abelian | C22×C3×C4×C72×C9 |
| multiplicative | (ℤ/23693)ˣ, (ℤ/25781)ˣ, (ℤ/26999)ˣ, (ℤ/27305)ˣ, (ℤ/31115)ˣ, (ℤ/33147)ˣ, (ℤ/33669)ˣ, (ℤ/38367)ˣ, (ℤ/47386)ˣ, (ℤ/51562)ˣ, (ℤ/53998)ˣ, (ℤ/54610)ˣ, (ℤ/62230)ˣ, (ℤ/66294)ˣ, (ℤ/67338)ˣ, (ℤ/76734)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C32×C72 |
| socle, prime radical | C23×C32×C72 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2700 conjugacy classes of subgroups.
21168 conjugacy classes. The character table is too large to display.
| automorphism group of | C19×C29×C43 |
| outer automorphism group of | C19×C29×C43 |
Past the SmallGroups library coverage — no SmallGroups id.