Finite Group DatabasebetaFinite Group Databasebeta| order | 31640 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 451584 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C5×C7×C113 |
| multiplicative | (ℤ/48351)ˣ, (ℤ/52239)ˣ, (ℤ/64468)ˣ, (ℤ/69652)ˣ, (ℤ/96702)ˣ, (ℤ/104478)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
128 conjugacy classes of subgroups.
31640 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.