Finite Group DatabasebetaFinite Group Databasebeta| order | 27648 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 17666408448 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C33×C4 |
| abelian | C22×C33×C4×C64 |
| multiplicative | (ℤ/52689)ˣ, (ℤ/60795)ˣ, (ℤ/70252)ˣ, (ℤ/90324)ˣ, (ℤ/105378)ˣ, (ℤ/121590)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C32 | C24×C33 |
| socle, prime radical | C24×C33 | C2×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
21644 conjugacy classes of subgroups.
27648 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.