Finite Group DatabasebetaFinite Group Databasebeta| order | 25920 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 160526499840 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C9 |
| abelian | C24×C4×C5×C92 |
| multiplicative | (ℤ/61864)ˣ, (ℤ/82536)ˣ, (ℤ/87912)ˣ, (ℤ/90288)ˣ, (ℤ/92796)ˣ, (ℤ/102600)ˣ, (ℤ/112860)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C32 | C25×C32×C5 |
| socle, prime radical | C25×C32×C5 | C2×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
31326 conjugacy classes of subgroups.
25920 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.