Finite Group DatabasebetaFinite Group Databasebeta| order | 19200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 84557168640 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C29×C4×C5 |
| abelian | C23×C3×C4×C52×C8 |
| multiplicative | (ℤ/46904)ˣ, (ℤ/47355)ˣ, (ℤ/50512)ˣ, (ℤ/50840)ˣ, (ℤ/54560)ˣ, (ℤ/57400)ˣ, (ℤ/60024)ˣ, (ℤ/61008)ˣ, (ℤ/61600)ˣ, (ℤ/63140)ˣ, (ℤ/64416)ˣ, (ℤ/64944)ˣ, (ℤ/70356)ˣ, (ℤ/73800)ˣ, (ℤ/74400)ˣ, (ℤ/76260)ˣ, (ℤ/79200)ˣ, (ℤ/81180)ˣ, (ℤ/86100)ˣ, (ℤ/94710)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C25×C3×C52 |
| socle, prime radical | C25×C3×C52 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
37104 conjugacy classes of subgroups.
19200 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.