Finite Group DatabasebetaFinite Group Databasebeta| order | 6912 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4459069440 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C3 |
| abelian | C24×C3×C9×C16 |
| multiplicative | (ℤ/18088)ˣ, (ℤ/23256)ˣ, (ℤ/25536)ˣ, (ℤ/25704)ˣ, (ℤ/27132)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C8 | C25×C32 |
| socle, prime radical | C25×C32 | C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12950 conjugacy classes of subgroups.
6912 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.