Finite Group DatabasebetaFinite Group Databasebeta| order | 29520 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1474560 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C4×C5×C41 |
| multiplicative | (ℤ/33449)ˣ, (ℤ/35441)ˣ, (ℤ/43085)ˣ, (ℤ/45567)ˣ, (ℤ/48009)ˣ, (ℤ/51723)ˣ, (ℤ/55395)ˣ, (ℤ/64012)ˣ, (ℤ/66898)ˣ, (ℤ/70882)ˣ, (ℤ/86170)ˣ, (ℤ/91134)ˣ, (ℤ/96018)ˣ, (ℤ/103446)ˣ, (ℤ/110790)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C32×C5×C41 |
| socle, prime radical | C23×C32×C5×C41 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
29520 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.