Finite Group DatabasebetaFinite Group Databasebeta| order | 25920 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 13377208320 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C3 |
| abelian | C24×C3×C4×C5×C27 |
| multiplicative | (ℤ/67144)ˣ, (ℤ/75880)ˣ, (ℤ/81096)ˣ, (ℤ/84552)ˣ, (ℤ/86328)ˣ, (ℤ/90888)ˣ, (ℤ/91056)ˣ, (ℤ/92664)ˣ, (ℤ/97560)ˣ, (ℤ/99792)ˣ, (ℤ/100440)ˣ, (ℤ/100716)ˣ, (ℤ/113400)ˣ, (ℤ/113820)ˣ, (ℤ/124740)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C9 | C25×C32×C5 |
| socle, prime radical | C25×C32×C5 | C2×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
19068 conjugacy classes of subgroups.
25920 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.