Finite Group DatabasebetaFinite Group Databasebeta| order | 31040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 56623104 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C42×C5×C97 |
| multiplicative | (ℤ/64185)ˣ, (ℤ/68464)ˣ, (ℤ/77680)ˣ, (ℤ/77800)ˣ, (ℤ/85580)ˣ, (ℤ/116700)ˣ, (ℤ/128370)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C24×C5×C97 |
| socle, prime radical | C24×C5×C97 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
996 conjugacy classes of subgroups.
31040 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.