Finite Group DatabasebetaFinite Group Databasebeta| order | 29520 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 154828800 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C24×C32×C5×C41 |
| multiplicative | (ℤ/54033)ˣ, (ℤ/57519)ˣ, (ℤ/68936)ˣ, (ℤ/72044)ˣ, (ℤ/88632)ˣ, (ℤ/92628)ˣ, (ℤ/103404)ˣ, (ℤ/108066)ˣ, (ℤ/115038)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1608 conjugacy classes of subgroups.
29520 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.