Finite Group DatabasebetaFinite Group Databasebeta| order | 19200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6039797760 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C43×C5 |
| abelian | C2×C3×C42×C52×C8 |
| multiplicative | (ℤ/29315)ˣ, (ℤ/37515)ˣ, (ℤ/39975)ˣ, (ℤ/40016)ˣ, (ℤ/48800)ˣ, (ℤ/50020)ˣ, (ℤ/53300)ˣ, (ℤ/58630)ˣ, (ℤ/75030)ˣ, (ℤ/79950)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C4 | C24×C3×C52 |
| socle, prime radical | C24×C3×C52 | C22×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
16368 conjugacy classes of subgroups.
19200 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.