Finite Group DatabasebetaFinite Group Databasebeta| order | 9360 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4608 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C5×C8×C9×C13 |
| multiplicative | (ℤ/9563)ˣ, (ℤ/9899)ˣ, (ℤ/10307)ˣ, (ℤ/14067)ˣ, (ℤ/19126)ˣ, (ℤ/19798)ˣ, (ℤ/20614)ˣ, (ℤ/28134)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C22×C3×C5×C13 |
| socle, prime radical | C22×C3×C5×C13 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
132 conjugacy classes of subgroups.
9360 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.