Finite Group DatabasebetaFinite Group Databasebeta| order | 28800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4529848320 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4×C5 |
| abelian | C22×C32×C4×C52×C8 |
| multiplicative | (ℤ/41041)ˣ, (ℤ/44485)ˣ, (ℤ/49569)ˣ, (ℤ/52521)ˣ, (ℤ/52767)ˣ, (ℤ/57195)ˣ, (ℤ/60512)ˣ, (ℤ/64575)ˣ, (ℤ/66092)ˣ, (ℤ/70028)ˣ, (ℤ/82082)ˣ, (ℤ/88970)ˣ, (ℤ/90036)ˣ, (ℤ/99138)ˣ, (ℤ/105042)ˣ, (ℤ/105534)ˣ, (ℤ/114390)ˣ, (ℤ/129150)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C24×C32×C52 |
| socle, prime radical | C24×C32×C52 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
18240 conjugacy classes of subgroups.
28800 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.