Finite Group DatabasebetaFinite Group Databasebeta| order | 22140 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 103680 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C22×C3×C5×C9×C41 |
| multiplicative | (ℤ/22909)ˣ, (ℤ/23389)ˣ, (ℤ/25837)ˣ, (ℤ/33219)ˣ, (ℤ/33237)ˣ, (ℤ/45818)ˣ, (ℤ/46778)ˣ, (ℤ/51674)ˣ, (ℤ/66438)ˣ, (ℤ/66474)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C22×C32×C5×C41 |
| socle, prime radical | C22×C32×C5×C41 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
200 conjugacy classes of subgroups.
22140 conjugacy classes. The character table is too large to display.
| automorphism group of | C31×C739, C19×C1231 |
| outer automorphism group of | C31×C739, C19×C1231 |
Past the SmallGroups library coverage — no SmallGroups id.