Finite Group DatabasebetaFinite Group Databasebeta| order | 17760 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 442368 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C3×C42×C5×C37 |
| multiplicative | (ℤ/21307)ˣ, (ℤ/23095)ˣ, (ℤ/26075)ˣ, (ℤ/27267)ˣ, (ℤ/33315)ˣ, (ℤ/33525)ˣ, (ℤ/35536)ˣ, (ℤ/36356)ˣ, (ℤ/42614)ˣ, (ℤ/44420)ˣ, (ℤ/46190)ˣ, (ℤ/52150)ˣ, (ℤ/54534)ˣ, (ℤ/66630)ˣ, (ℤ/67050)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C23×C3×C5×C37 |
| socle, prime radical | C23×C3×C5×C37 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
432 conjugacy classes of subgroups.
17760 conjugacy classes. The character table is too large to display.
| automorphism group of | C11×C13×C149 |
| outer automorphism group of | C11×C13×C149 |
Past the SmallGroups library coverage — no SmallGroups id.