Finite Group DatabasebetaFinite Group Databasebeta| order | 21744 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1382400 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C4×C151 |
| multiplicative | (ℤ/31745)ˣ, (ℤ/35373)ˣ, (ℤ/40815)ˣ, (ℤ/47164)ˣ, (ℤ/63490)ˣ, (ℤ/70746)ˣ, (ℤ/81630)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C32×C151 |
| socle, prime radical | C23×C32×C151 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
324 conjugacy classes of subgroups.
21744 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.