Finite Group DatabasebetaFinite Group Databasebeta| order | 25920 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 995328 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C3×C5×C16×C27 |
| multiplicative | (ℤ/32249)ˣ, (ℤ/33341)ˣ, (ℤ/40269)ˣ, (ℤ/41463)ˣ, (ℤ/42687)ˣ, (ℤ/42867)ˣ, (ℤ/45381)ˣ, (ℤ/53692)ˣ, (ℤ/60508)ˣ, (ℤ/64498)ˣ, (ℤ/66682)ˣ, (ℤ/77796)ˣ, (ℤ/78084)ˣ, (ℤ/80538)ˣ, (ℤ/82926)ˣ, (ℤ/85374)ˣ, (ℤ/85734)ˣ, (ℤ/90762)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8×C9 | C23×C32×C5 |
| socle, prime radical | C23×C32×C5 | C8×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1372 conjugacy classes of subgroups.
25920 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.