Finite Group DatabasebetaFinite Group Databasebeta| order | 27648 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 152202903552 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C29×C3×C8 |
| abelian | C23×C3×C8×C9×C16 |
| multiplicative | (ℤ/69496)ˣ, (ℤ/72352)ˣ, (ℤ/89352)ˣ, (ℤ/93024)ˣ, (ℤ/98112)ˣ, (ℤ/102816)ˣ, (ℤ/104244)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4×C8 | C25×C32 |
| socle, prime radical | C25×C32 | C3×C4×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
60050 conjugacy classes of subgroups.
27648 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.