Finite Group DatabasebetaFinite Group Databasebeta| order | 25920 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4013162496 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C33 |
| abelian | C23×C32×C5×C8×C9 |
| multiplicative | (ℤ/47523)ˣ, (ℤ/49077)ˣ, (ℤ/50589)ˣ, (ℤ/63364)ˣ, (ℤ/81468)ˣ, (ℤ/95046)ˣ, (ℤ/98154)ˣ, (ℤ/101178)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C24×C33×C5 |
| socle, prime radical | C24×C33×C5 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
16900 conjugacy classes of subgroups.
25920 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.