Finite Group DatabasebetaFinite Group Databasebeta| order | 21888 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4756340736 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3×C43 |
| abelian | C2×C32×C43×C19 |
| multiplicative | (ℤ/44655)ˣ, (ℤ/47632)ˣ, (ℤ/59540)ˣ, (ℤ/89310)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23 | C24×C32×C19 |
| socle, prime radical | C24×C32×C19 | C23 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
7632 conjugacy classes of subgroups.
21888 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.