Finite Group DatabasebetaFinite Group Databasebeta| order | 21504 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 150994944 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C42×C16 |
| abelian | C3×C4×C7×C162 |
| multiplicative | (ℤ/24973)ˣ, (ℤ/28645)ˣ, (ℤ/49946)ˣ, (ℤ/57290)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C82 | C23×C3×C7 |
| socle, prime radical | C23×C3×C7 | C2×C82 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3636 conjugacy classes of subgroups.
21504 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C17×C113 |
| outer automorphism group of | C13×C17×C113 |
Past the SmallGroups library coverage — no SmallGroups id.