Finite Group DatabasebetaFinite Group Databasebeta| order | 31376 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 359424 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C37×C53 |
| multiplicative | (ℤ/47829)ˣ, (ℤ/58845)ˣ, (ℤ/62768)ˣ, (ℤ/63772)ˣ, (ℤ/78460)ˣ, (ℤ/95658)ˣ, (ℤ/117690)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C37×C53 |
| socle, prime radical | C23×C37×C53 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
108 conjugacy classes of subgroups.
31376 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.