Finite Group DatabasebetaFinite Group Databasebeta| order | 17136 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 73728 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C32×C7×C8×C17 |
| multiplicative | (ℤ/17587)ˣ, (ℤ/19999)ˣ, (ℤ/20041)ˣ, (ℤ/25713)ˣ, (ℤ/35174)ˣ, (ℤ/39998)ˣ, (ℤ/40082)ˣ, (ℤ/51426)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C22×C32×C7×C17 |
| socle, prime radical | C22×C32×C7×C17 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
264 conjugacy classes of subgroups.
17136 conjugacy classes. The character table is too large to display.
| automorphism group of | C43×C409, C7×C2857 |
| outer automorphism group of | C43×C409, C7×C2857 |
Past the SmallGroups library coverage — no SmallGroups id.