Finite Group DatabasebetaFinite Group Databasebeta| order | 27120 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 172032 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C5×C113 |
| multiplicative | (ℤ/32461)ˣ, (ℤ/35185)ˣ, (ℤ/39725)ˣ, (ℤ/41541)ˣ, (ℤ/50865)ˣ, (ℤ/51075)ˣ, (ℤ/54248)ˣ, (ℤ/54256)ˣ, (ℤ/55388)ˣ, (ℤ/64922)ˣ, (ℤ/67820)ˣ, (ℤ/70370)ˣ, (ℤ/79450)ˣ, (ℤ/81372)ˣ, (ℤ/83082)ˣ, (ℤ/101730)ˣ, (ℤ/102150)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C3×C5×C113 |
| socle, prime radical | C23×C3×C5×C113 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
216 conjugacy classes of subgroups.
27120 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.