Finite Group DatabasebetaFinite Group Databasebeta| order | 17136 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 9216 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C7×C8×C9×C17 |
| multiplicative | (ℤ/17399)ˣ, (ℤ/17447)ˣ, (ℤ/18107)ˣ, (ℤ/25731)ˣ, (ℤ/34798)ˣ, (ℤ/34894)ˣ, (ℤ/36214)ˣ, (ℤ/51462)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C22×C3×C7×C17 |
| socle, prime radical | C22×C3×C7×C17 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
132 conjugacy classes of subgroups.
17136 conjugacy classes. The character table is too large to display.
| automorphism group of | C127×C137, C73×C239, C19×C953 |
| outer automorphism group of | C127×C137, C73×C239, C19×C953 |
Past the SmallGroups library coverage — no SmallGroups id.