Finite Group DatabasebetaFinite Group Databasebeta| order | 29160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 839808 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C9 |
| abelian | C2×C4×C5×C9×C81 |
| multiplicative | (ℤ/29503)ˣ, (ℤ/30007)ˣ, (ℤ/30799)ˣ, (ℤ/43767)ˣ, (ℤ/43983)ˣ, (ℤ/59006)ˣ, (ℤ/60014)ˣ, (ℤ/61598)ˣ, (ℤ/87534)ˣ, (ℤ/87966)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C27 | C22×C32×C5 |
| socle, prime radical | C22×C32×C5 | C2×C3×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
784 conjugacy classes of subgroups.
29160 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.