Finite Group DatabasebetaFinite Group Databasebeta| order | 19200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7864320 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C43 |
| abelian | C3×C42×C16×C25 |
| multiplicative | (ℤ/22321)ˣ, (ℤ/26065)ˣ, (ℤ/27625)ˣ, (ℤ/44642)ˣ, (ℤ/52130)ˣ, (ℤ/55250)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C5×C8 | C23×C3×C5 |
| socle, prime radical | C23×C3×C5 | C22×C5×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1674 conjugacy classes of subgroups.
19200 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C17×C101, C13×C17×C125 |
| outer automorphism group of | C13×C17×C101, C13×C17×C125 |
Past the SmallGroups library coverage — no SmallGroups id.