Finite Group DatabasebetaFinite Group Databasebeta| order | 27216 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 76187381760 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C32×C9 |
| abelian | C24×C3×C7×C92 |
| multiplicative | (ℤ/50673)ˣ, (ℤ/67564)ˣ, (ℤ/86868)ˣ, (ℤ/88236)ˣ, (ℤ/96012)ˣ, (ℤ/100548)ˣ, (ℤ/101346)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C32 | C24×C33×C7 |
| socle, prime radical | C24×C33×C7 | C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
16884 conjugacy classes of subgroups.
27216 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.