Finite Group DatabasebetaFinite Group Databasebeta| order | 19200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 31457280 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C5×C8 |
| abelian | C2×C3×C52×C8×C16 |
| multiplicative | (ℤ/21607)ˣ, (ℤ/29643)ˣ, (ℤ/39524)ˣ, (ℤ/43214)ˣ, (ℤ/59286)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4×C8 | C23×C3×C52 |
| socle, prime radical | C23×C3×C52 | C4×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3184 conjugacy classes of subgroups.
19200 conjugacy classes. The character table is too large to display.
| automorphism group of | C17×C31×C41 |
| outer automorphism group of | C17×C31×C41 |
Past the SmallGroups library coverage — no SmallGroups id.