Finite Group DatabasebetaFinite Group Databasebeta| order | 6120 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 24576 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C32×C4×C5×C17 |
| multiplicative | (ℤ/6283)ˣ, (ℤ/7147)ˣ, (ℤ/9189)ˣ, (ℤ/12566)ˣ, (ℤ/14294)ˣ, (ℤ/18378)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C32×C5×C17 |
| socle, prime radical | C22×C32×C5×C17 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
192 conjugacy classes of subgroups.
6120 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.