Finite Group DatabasebetaFinite Group Databasebeta| order | 19200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 39636172800 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C5 |
| abelian | C24×C3×C52×C16 |
| multiplicative | (ℤ/46376)ˣ, (ℤ/63624)ˣ, (ℤ/65472)ˣ, (ℤ/69564)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C25×C3×C52 |
| socle, prime radical | C25×C3×C52 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
20720 conjugacy classes of subgroups.
19200 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.