Finite Group DatabasebetaFinite Group Databasebeta| order | 29640 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 290304 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C3×C5×C13×C19 |
| multiplicative | (ℤ/45267)ˣ, (ℤ/48939)ˣ, (ℤ/59288)ˣ, (ℤ/60356)ˣ, (ℤ/65252)ˣ, (ℤ/88932)ˣ, (ℤ/90534)ˣ, (ℤ/97878)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
256 conjugacy classes of subgroups.
29640 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.