Finite Group DatabasebetaFinite Group Databasebeta| order | 19200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 40960 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C3×C4×C25×C64 |
| multiplicative | (ℤ/19493)ˣ, (ℤ/20813)ˣ, (ℤ/24005)ˣ, (ℤ/24125)ˣ, (ℤ/38986)ˣ, (ℤ/41626)ˣ, (ℤ/48010)ˣ, (ℤ/48250)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C5×C32 | C22×C3×C5 |
| socle, prime radical | C22×C3×C5 | C2×C5×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
258 conjugacy classes of subgroups.
19200 conjugacy classes. The character table is too large to display.
| automorphism group of | C101×C193, C13×C1601 |
| outer automorphism group of | C101×C193, C13×C1601 |
Past the SmallGroups library coverage — no SmallGroups id.