Finite Group DatabasebetaFinite Group Databasebeta| order | 17160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7680 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C4×C5×C11×C13 |
| multiplicative | (ℤ/17543)ˣ, (ℤ/18997)ˣ, (ℤ/20027)ˣ, (ℤ/20449)ˣ, (ℤ/21475)ˣ, (ℤ/25743)ˣ, (ℤ/25749)ˣ, (ℤ/34324)ˣ, (ℤ/35086)ˣ, (ℤ/37994)ˣ, (ℤ/40054)ˣ, (ℤ/40898)ˣ, (ℤ/42950)ˣ, (ℤ/51486)ˣ, (ℤ/51498)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C3×C5×C11×C13 |
| socle, prime radical | C22×C3×C5×C11×C13 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
128 conjugacy classes of subgroups.
17160 conjugacy classes. The character table is too large to display.
| automorphism group of | C53×C331, C7×C2861 |
| outer automorphism group of | C53×C331, C7×C2861 |
Past the SmallGroups library coverage — no SmallGroups id.