Finite Group DatabasebetaFinite Group Databasebeta| order | 21384 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1058158080 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C32×C9 |
| abelian | C23×C3×C92×C11 |
| multiplicative | (ℤ/26467)ˣ, (ℤ/34029)ˣ, (ℤ/34371)ˣ, (ℤ/37611)ˣ, (ℤ/52934)ˣ, (ℤ/68058)ˣ, (ℤ/68742)ˣ, (ℤ/75222)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C32 | C23×C33×C11 |
| socle, prime radical | C23×C33×C11 | C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4032 conjugacy classes of subgroups.
21384 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.