Finite Group DatabasebetaFinite Group Databasebeta| order | 17160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 161280 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C3×C5×C11×C13 |
| multiplicative | (ℤ/19987)ˣ, (ℤ/21091)ˣ, (ℤ/26331)ˣ, (ℤ/27117)ˣ, (ℤ/28347)ˣ, (ℤ/28677)ˣ, (ℤ/35108)ˣ, (ℤ/37796)ˣ, (ℤ/38236)ˣ, (ℤ/39974)ˣ, (ℤ/42182)ˣ, (ℤ/52662)ˣ, (ℤ/54234)ˣ, (ℤ/56694)ˣ, (ℤ/57354)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
256 conjugacy classes of subgroups.
17160 conjugacy classes. The character table is too large to display.
| automorphism group of | C7×C23×C131 |
| outer automorphism group of | C7×C23×C131 |
Past the SmallGroups library coverage — no SmallGroups id.