Finite Group DatabasebetaFinite Group Databasebeta| order | 19200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 983040 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C16 |
| abelian | C3×C162×C25 |
| multiplicative | (ℤ/20417)ˣ, (ℤ/40834)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C5×C82 | C22×C3×C5 |
| socle, prime radical | C22×C3×C5 | C5×C82 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
498 conjugacy classes of subgroups.
19200 conjugacy classes. The character table is too large to display.
| automorphism group of | C17×C1201 |
| outer automorphism group of | C17×C1201 |
Past the SmallGroups library coverage — no SmallGroups id.