Finite Group DatabasebetaFinite Group Databasebeta| order | 25920 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 165888 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C5×C16×C81 |
| multiplicative | (ℤ/30481)ˣ, (ℤ/41361)ˣ, (ℤ/42801)ˣ, (ℤ/45441)ˣ, (ℤ/51848)ˣ, (ℤ/51904)ˣ, (ℤ/55148)ˣ, (ℤ/57068)ˣ, (ℤ/60962)ˣ, (ℤ/77772)ˣ, (ℤ/82722)ˣ, (ℤ/85602)ˣ, (ℤ/90882)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8×C27 | C23×C3×C5 |
| socle, prime radical | C23×C3×C5 | C8×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
490 conjugacy classes of subgroups.
25920 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.